I've seen some games use a reverse of that mechanic, where having lower health will actually make you do *more* damage. For example:

Teenage Mutant Ninja Turtles (NES): When below half health, 3 of the turtles do double damage.

Final Fantasy 6: The Valiant Knife does more damage when HP is lower, and there's a blue magic spell that works like that as well. That blue magic spell also exists in FF5 (though annoyingly it can miss).

Lufia 2: When you get hit, your IP (used for special abilities that are found on equipment) increases based on the percentage of current health that you lost. (Final Fantasy 7 sort-of copied this, but the limit meter only fills based off the percentage of *maximum* health lost, which I don't think is as interesting a mechanic.)

Final Fantasy 8: Limit breaks work best when at low health (and don't show up at high health unless you cast Aura).

Castlevania: Aria of Sorrow: There is one soul that increases your attack power when your HP is low.

I am ok with up to 6 stats but more than that and it's difficult for me to keep track of. If there is agility + dexterity or speed or accuracy, I always forget the use of each.

Btw in games that use the d&d rules, I hate it that there are some mostly useless stats. Why do they put intelligence in there if it's only important for mages and why is charisma there if it is only important for the leader? I would prefer an easier / simpler way

Never played it but that actually sounds pretty neat. Guess it's about time that I check the game out.

Stats in games are used in combat, as input for formulas, and out of combat, for binary results. The problem you solve here is the combat output being a non-continuous function.
(Noncombat binary success/failure can also be randomized, but even in many roguelikes the outcomes are so important they aren't left to chance because the swinginess would depreciate tactical skill; a classic RPG player can just reload).

But the other problem is character optimization (with regards to combat effectiveness). It can be as continuous as the underlying math engine allows, but the number of maxima is finite and low. Maxing out the INT of a single-class wizard whose spells all work off INT isn't a choice. The assumption goes that players are trying to win the game, and the target audience for a combat encouter is going to be these maxed-out characters: "the boss encouter of dungeon 3 is a green dragon, so we expect the party to have Attack 25, either Dodge 14 or elemental damage reduction, and 2nd-tier spells". Leaving the option to not max out serves no purpose.

The end result of designing a combat system in an RPG is a set of available actions with their associated resource costs and chances of success; a character generation system adds restrictions on which subsets of actions are available on individual characters. When you have this math construct and made sure it works, it doesn't need to be retroactively justified by making the ideal output a fake function of some other numbers, and especially it doesn't need to be broken by adding more moving parts.

Fighter-mages as multi-attribute dependency (MAD) builds have historically not worked well (or, indeed, at all). MAD breaks the system's benchmarks.
- Absent combos between things humanity was not meant to combo, a MAD character is dead weight.
- If combos exist, there's absolutely no guarantee the character would be in line with a single-class wizard or single-class warrior (while a sliding scale of physical attack stat vs magical attack stat isn't what causes the problem -- multi-"classing" does -- it certainly doesn't help). If, say, there's a "wizard" INT spell that delivers a nasty touch (requiring a squishy wizard to be next to an enemy and hit with a 1/round attack) and you get that spell on an archer precision-shooting 20 arrows per round at targets up to 3 miles in range, it's a problem, and one that might not be isolated and fixed beforehand because the amount of possible combos is some crazy combinatorial number with a Hungarian surname.

So if you want a spellsword, it should just be a separate class. If you feel the advantage of having a choice between a magical and a physical attack on a single character needs to be accounted for, you can just make a spellsword's attacks less powerful by changing numbers as you see fit, by amounts that you can adjust independently, without wrecking the foundations of the system.

As for equipment bonuses, they can just modify the important characteristics directly, from scaling effects across the board to spot-modifying specific abilities. So a ring of INT +2 would be a ring of power +2 that adds two levels to pell effect calculations. It also means it can't be easily given to a rogue to increase disarm traps, but exactly because stat increase items need to play it safe and provide "balanced" gains in the best use case, they have never been much fun. (Example: suppose paladin healing works off INT, which is usually low because they don't have much else to do with INT. A massive INT bonus item that'd allow a paladin to drop a huge meaningful party heal is nice, but it'd also allow a wizard to nuke each and every encounter. On the other hand, what's a meaningful overcap bonus to a wizard would be a waste of slot for a paladin because a better use of an action would be still "bash a sinner's face in with a warhammer and pray for a crit".)

Learn by doing linear games are either optimization nightmares (if they don't allow grinding) or purposefully forgo target difficulty as a design tenet (if they do) and I'm not going there.

This reminds me of one thing: I consider trap disarming to be a poor mechanic in RPGs. Pretty much, it works out to a "must have this class in your party" mechanic, and not in an emergent way (unlike, say, healing magic). I am of the opinion that traps should either be non-existent or not disarmable with a generic disarm skill. (My favorite use of traps in a game would be something like Syoban Action, which has practically nothing in common with the games people call RPGs.)

Here's a question: Suppose you have a mage with 20 INT and 2 END, who, while effective, keeps being one hit killed by enemies. Also, suppose you have 20 skill points, and raising a stat requires a number of skill points equal to the old value in the stat. So, in this case, you have (at least) two options to spend your skill points. Do you:

1. Raise your INT by 21, giving them a marginal (only 5%) increase in spell damage, or

2. Raise your END to 7, drastically increasing their HP, allowing them to actually take a hit without dying?

(Let's assume you don't see any other good use of skill points.)

As one can see, when the cost of increasing a stat increases the higher it is, maybe maxing out a stat isn't the best use of skill points. (I note that the old Avernum games (not the newer remakes) have skill point costs scale in a similar, albeit slower, manner.)

Another approach I have seen is in the game I was just playing, Dust: An Elysian Tail. In this game, skill points are called Skill Gems, and your highest stat can't exceed your lowest by more than 4 Skill Gems; this makes it so that you can't become too hyper-focused in one stat, and so that you do have to boost your other stats.

This reminds me of a situation in the game Chrono Trigger. One of the characters, Ayla, is meant to be a pure physical character, but she happens to have a cheap healing techl, which happens to be the only tech that can cure status ailments (not counting a certain Double Tech that involves this tech). Of course, Ayla has the lowest magic stat, so to make this ability heal a decent amount, the developers actually gave this skill a pretty high multiplier.

The game includes a consumable item called a Magic Tab, which permanently boosts a character's magic stat by one. Using it on, say, Marle or Lucca will only provide a small boost to their magic abilities (and neither needs any to eventually max this stat), but giving it to Ayla will noticeably increase the power of her healing ability.

(I also note that the choice isn't between STR or MAG with Ayla, but rather a choice between MAG for Ayla or MAG for someone else, like Chrono or Robo, both of whom also get decent use out of them.)

That hasn't always been my experience. In particular, the DS remake of SaGa 3 seems to be reasonably balanced when it comes to difficulty (at least as well as other JRPGs that use traditional leveling), and SaGa Frontier 2 seems reasonable except for one army battle (where your main character's stats are irrelevant) and the final boss (who might be a bit too difficult if you don't train extra). Both games do allow what you refer to as "grinding" (though in SaGa Frontier 2 it gets a bit tricky to do so).

By the way, the original SaGa is not a learn by doing game; stat growth in that game is definitely unusual, but it is independent of your actions (unless you count RNG manipulation as "actions" here).

As long as they work I don't care. I've played lots and lots of different RPG's and liked most of them and the ones I didn't like I wouldn't say it was because of the Stats system used.

That said, one of the things I disliked the most about the early Fallout's was that the stats you started out with you basically ended up with. (with some exception). I much prefer characters that evolve in not only skills but stats as well. A good example is strength. It seems really odd that a character stays the same strength the whole game. What, he doesn't grow at all? No workouts of any kind? But having said all of that..... Fallout 1 and 2 were my favorite games of all time for quite a few years (until I finally played Gothic 1 and 2). So see, that's how... unimportant.. overall stats are to me. Just make them work, don't make them meaningless, and I'm okay. Plus it's fun when different games use different systems.

Want a really strange one try Betrayal at Krondor (which was my favorite game of all time until I finally played Fallout). You can change skills by using them but I've never yet been able to figure out how strength and hit points changes. But they do. I wanted to say it's chapter based, but if it is it must be different for different characters because I swear it always seemed like Gorath's stats went up faster than anyone else's. Then there for awhile I was convinced it was based on in-game days the character played. But that could be another of those mis-perceptions on my part, or maybe faulty memory I dunno.

Anyway, if you look at those first three games that I placed on my ALL TIME FAVORITE OF ANY GENRE game, those three are vastly different from each other in how they use and do stats.. Again showing how... unimportant??? doesn't feel like the right word.. stats are in determining whether or not I like a game.