Why, you thinking of developing one?
Shadowrun Returns is a turn-based "tactical" RPG. In this, your party/team generally gets to move before the enemy does. The system pre-determines character order. If you mix player & enemy moves it would make it easier to predict tactics as each move occurs, and you could counter it, character for character. IMO, it's a better match if you follow Shadowrun's example.

I might develop one, but (assuming I ever get around to doing so) one important difference is that it will not be tactical; position will not be part of the battle system.

Your explanation of mixing player and enemy moves only works if commands are executed immediately; if you have to choose your commands before the start of the round, you can't reliably counter enemy actions (particularly if turn order isn't completely deterministic); you can also get situations where an enemy silenced your healer before she could cast her healing spell, resulting in a wasted turn and your party perhaps getting into a rather dicey situation.

I like the way StarCrawlers handles it:

There is basically a "battle queue" which shows the turn order of PCs and enemies. Every action costs time units (faster characters use less time units for actions) which determine how far back into the queue the actor goes.

So for instance an enemy chooses to charge some super-attack which costs them 50 time units, my character using a quicker attack (20 TU) will attack twice before the super attack is charged - possibly killing the enemy before they can strike.

Or, I can use a powerful buff for my party - but it will place the character far back in the queue, or decide to use some weaker "spell" but will get my turn back faster with this character.

This system leads to an interesting dynamic comparable to the RTB system of some JRPGs while staying completely turn-based.

Problems with this:
1. I think having speed give characters more actions over time isn't the best mechanic; it tends to overvalue the speed attribute and it might have scaling issues at high values (specifically, if speed increases at level up, it makes levels have more of an effect on the battle, making it much harder for an underleveled party to win a fight).
2. Screen space is limited, so if there are enough battle combatants, you can have a situation where characters don't show up in the queue due to there being too many other combatants who get to act. For instance, if the party is fighting 396 berserkers, and maybe 5% will get to act before the next party member's turn, there won't be room to show which party members get to act next. (Yes, if I actually write the game, I might want to support encounters with this many enemies.)

Definitely not random but also a little RNG should be involved - like in "real life".

Turn order should be determined by some stat - agility / speed are good examples.

There should be not turns per se, just order of movement.

Example: There are two parties with three characters each, lets call them A1, A2, A3 and B1, B2, B3.
They have different "speed/agility" stats, for example A1=1, A2=2, A3=5, B1=3, B2=8, B3=5, where 1 is the fastest, 10 is the slowest. 1 in stat also means that this character is 10 times faster than character with 10 in stat.

If we take the order of 10 movements, A1 can move 10 times and A3 only 5 times during this period of time.
In the end, after calculations and "a little of RNG" A1 can move 9 times and A3 6 times during the same period of time.

1. I disagree. Not making faster characters have more turns means that speed is pretty much useless, except for possibly determining first round order. Which is very close to meaningless in a very long battle, like it would certainly be if you had 396 opponents.

2. Screen space can be unlimited, depending on the presentation you choose. For example, scrollbars exist. Do not think that I'm saying you should use one but that there are ways around this limitation.

I never liked the "delayed action" TB system. So in universe your white mage decided to heal but the character she was going to heal dies and she doesn't notice it and wastes her turn? She's obviously brain damaged. And so is the rest of my party, and my enemies too, because they all act like that one time or another. Excuse me but I prefer that both me and the enemies I'll defeat to be smarter and more capable.
A "delayed action" TB system implies all that. Feels like a very half-assed gameplay system to me.

I think the turn-based queue system I liked the most was Final Fantasy Tactics's. I won't spend time with an explanation as I know you're familiar with that game. It was pretty good at giving me the opportunity to create strategies (who to attacks next, who should I heal, etc.)
Granted, (among several game-breakers) speed could be abused in FFT to give your characters a hundred turns before the enemy's next turn, but you can just not create such loopholes, you know.

Edit: Tho, just as Lexor said I'd include some RNG for good measure in my game design. If I were making a TB game, you know.

Problem is that I find that this sort of mechanic makes the speed stat too important; it also doesn't scale well. Imagine if, say, A1 has 500 speed and A2 has 35,000 speed; in this case, A1 is unlikely to ever get a chance to act before A2 single-handedly resolves the combat (or the player becomes impatient).

Also, another thought occurred to me: If stat growth is dependent on taking actions and higher speed characters get more actions, higher speed characters will get stat gains faster, which will result in an inbalance between characters growing more severe as times goes on (which is the opposite of the effect I want; I want newly created characters to catch up to old characters, or at least become useful, reasonably quickly). When that first action allows for one to wipe out the entire enemy party, or at least a large portion of it, before they get to act, speed does matter.

Also (assuming commans entered at the beginning of the round), high speed can be useful for healers; a fast healer can heal an injured character before an enemy gets a chance to finish off the character. (Of course, there's also situations where low speed can be useful for a healer, particularly when using multi-target healing, so the healer can hearl *after* the enemies do damage to the party.) There's also status ailments and other ways in which an action earlier in the round will affect those later in the round. (Interestingly enough, I can think of two games, Wasteland and Magic of Scheherezade, where ranged combat is treated as being simultaneous, so being killed by a ranged attack doesn't negate the ranged attack you're making this round.)

So you should carefully balance these numbers. 500 and 35,000 are pretty extreme: 70 turns from one character berofe the other has one. What if they were 500 and 435?

As for the char level up drift, that's a good consideration I still have to think about. There could be a way to counter it, but I don't have an answer on the spot.

I can think of a different in-universe explanation here: The white mage decides to heal an injured companion, and rushes over to save them, but unfortunately, she's too slow and the enemy gets to the companion first and slays them. At this point, the white mage has already started casting the spell, but doesn't get it off in time, wasting the magic and her turn, as there's no time to heal another character (or do something else) before the combat round is over.

(I note that this situation can happen in Final Fantasy Tactics, if using a spell with non-zero casting time (as opposed to a potion or Math Skill) to heal, and an enemy gets a turn before the spell goes off. On the other hand, I can't think of a good in-universe explanation for Math Skill, except that it involves complex mechanisms that only a Calculator can understand in-universe.) Have you played Phantom Brave? That game has an FFT-like action queue (albeit with all actions finishing instantly), but allows stat differences as big (and bigger, actually) than the example I gave. (I think there's some diminishing returns in the formula for turn fequency based on speed to try and temper this a little bit.)

I actually remember one leveling strategy in Phantom Brave: There's one map with an enemy that levels up every turn, and will not move until you get close to it. Hence, if you kill everything else and have Marona alone away from the enemy, you can just let the enemy gain levels. Eventually, it will reach the point where the enemy gets hundreds of turns for every one of yours, and the enemy will level up on each one of those turns, creating a very loud "level up" sound (might be a good idea to turn down the volume on the TV). Of course, there's the small matter of killing the enemy afterwords, but fortunately the enemy's current HP doesn't exist, and there's a passive skill called Big Bang that does damage ignoring enemy defense.

Thank you. Sounds interesting.

As for the topic:
I like how "Dead in Vinland" does it. It is based on your "initiative". Initiative can change through buffs and defuffs in the battle itself or through events outside of battle. For example: Some sickness/wound gives an initiative penalty or a "good mood" gives an initiative increase during non-battle events and they last for X day/s and only matter if you battle while they are in effect. Also you can get a permanent buff if you get a +X inititive choice option on level up. Or using a skill in battle gives you or an ally an initiative penalty/increase / an enemy inititive penalty and the effects last X turn/s in that battle only and comes into effect with the next starting round.
It is somewhat predictable, but still leaves room for flexibility and surprises to keep things interesting.

[1] Well if you have such an uberpowerful unbeatable tank of a char capable of in a single or even two attacks wipe out the enemy force you have balancing problems which far outweigh whatever issues arise from speed. That char obviously need nerfing, STAT.

[2] So you think that high speed should be the way to "counter" that brain damage situation from my earlier post?
Okay, then that particular white mage doesn't appear brain damaged because she's fast enough to get her spell out before the events make it evident that she is brain damaged. :)
The rest of the party tho will still appear just as much. Or whoever is not THE fastest thing in the battlefield.

As for a lower speed, it indeed can be useful in those situations you described. It still doesn't beat the fact that, in a "immediate action" system if the healer's turn comes up in a later part of the round she can get her spell out to do the exact same things as in your delayed action scenario, with the added benefit of making sure her turn is not wasted.

Edit: will read more of this thread and reply to Dtgreene's reply later, but now I have to work.

Final Fantasy did it right. Turns are random with a bonus for certain stats, and if a command attacks an enemy that dies or flees before the attack is executed, the attack fails instead of moving on to the next eligible target.

That's what I was thinking as I read the opening post. Stats as a base and then a little randomness thrown in: maybe someone fumbled a bit drawing the sword, their head was turned the wrong way, intuition alerted someone a bit sooner... that sort of explanation for it. I would add something like a Perception stat to that. First you notice the threat and then you react. That would apply after the initial round, also, as Perception might let the character find an opening sooner than others within the rounds of the fight.

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Nice thing about turn-based combat is that the designers can put in any number of systems / rules for this. They could keep a simple Speed stat mechanic, or get all sort of crazy with Speed, Level, Perception, Morale, Perks (both good and bad), wounds / hit point level, equipped item, skill level with that item type, environmental factors, type of enemy (animal-type enemies getting a bonus against humanoids, for example), and more.

It's not the thing of specific mechanics, it's the thing of the game design - if the game is wisely planned then every stats is on similar level of importance and then you can indeed end with "slow fighter" but on the other side, for example, great traps finder. Again, it's basic design of the game that holds it all together. It should not be so easy to reach high level of some stats without hard work (like every next level requires a lot more experience and time). Some RPGs do not use big numbers and they set some limits (18 per stat was max in old AD&D). Big numbers look nice on the paper (and for the player) indeed, but there is no reason to use them if there is no real difference between, for example, 35000 and 34900.