Yes, I do this -- it's part of how I role play -- but only in relatively safe areas like Beregost or Waukeen's Promenade. Putting aside your tactical considerations, it doesn't make sense to do it out in the wilds. But I would guess the majority of players keep the party together at all times.

I never thought about it that much, but I did like to explore Baldur's Gate like that, it felt more dynamic and alive.

I actually do that. If a member of my party is a thief, he'll be out breaking into houses and stealing things while the others are having a drink at the local tavern. I usually operate during the day. Sometimes I would go out at night for different reasons but I mostly sleep until daylight then go questing. Another exception to my daytime thing is dungeons. My party wouldn't know what time of day it is if they spend a lot of time in some villain's basement.

I'd sometimes use my thief (Imoen) for spying. (SPOLIERS FOLLOW !!!!!!!!!)

Once on my second run through I got bored with sending my entire party down the narrow deserted tombs that marked the beginning of the Candlekeep dungeon. Until the final one where Imoen was killed by two teleporting (Astral ?) spiders. Reload time. And the baleful realisation that I'd walked into that particular trap EXACTLY as the devs had intended.

Sending the thief ahead spying was far more common in Icewind Dale where enemy monsters would just be clustered together not moving until they saw the party. Of course with good judgement they'd be in range for a fireball blast without my party being "seen".

Of course that VERY nasty Demon from Tales of the Sword Coast needed you to split the party up to beat it. That by a long way was the toughest battle I had in the entire saga.

Otherwise no - trying to simultaneously manage party members in different parts of the map was a pain in the rump - and an unnecessary one.

S.x.

Actually, in BG2 you could do this with a mage or with the Wizard Eye spell.

With a Mage:
Cast Invisibility to prevent enemies from seeing you. (Improved Invisibility isn't necessary here, and regular Invisibility lasts longer.
Cast Protection from Magic: Divination to block True Sight/Seeing so that those enemies aren't able to discover you.
If using a Cleric/Mage (Aerie comes to mind here), you can cast Find Traps so you can see (but not disarm) traps
Enemy thieves using Detect Illusions can foil this setup (but how often do you encounter that?)
This *will* trigger scripts.

With Wizard Eye:
Just have the Wizard Eye scout.
This can be used to safely lure enemies who can see invisibility to the party.
This *will not* trigger scripts.
You do have to worry about gaze attacks. In Spellhold, a certain trap that crushes anything that enters counts as a gaze attack. (I have died as a result of this.) (Was this fixed in the fixpack or the Enhanced Edition?)
Once you've located the enemies, you can use Farsight + summons to kill the enemy before the enemy's opening dialogue triggers.

Anyway, the main reason to manage party members in different parts of the map is that it saves time. Keep in mind that in a speedrun, you will want the party to be hasted as much as possible, making things even more chaotic.

Even more ridiculous is managing characters who aren't on the same map. (Sometimes dismissing a party member, changing maps, and accepting the character's offer to rejoin can cause this situation.)

One other thing you sometimes see in speedruns is dead characters not being revived right away. The advantage of keeping a character dead is that you don't need to worry about the character's location; just one fewer character to manage, and when the dead character is needed, just revive him or her. (Remember that Irenicus Dungeon Imoen will leave if you try to HP kill her or if you cast Raise Dead/Harper's Call on her, even if you're not in Irenicus's Dungeon anymore.)

In BG1 I tend to split my party up more than in BG2. In BG1, I often send someone out ahead to scout out the area, especially my thief to detect traps, or my best warrior(s) to protect my weaker party members. And there are also more areas that are a tight fit for parties in BG1 that lead to not bringing everyone along all the time because they simply don't all fit very well in the space together.

In BG2 there are only a few areas where I split up my party. One example is when you go to feed the Umber Hulks in the De'Arnise Hold's dungeon. Or to keep Jaheira out of the Sea's Bounty in the Docks district, until I'm ready to deal with Baron Ployer's curse, so I don't have to interrupt what I was doing to go cure Jaheira right away. Those are the only examples I can think of off the top of my head where I split up my party in BG2 although there may be a few other times.

This sort of thing, having to interrupt what you're doing, is one of the many reasons I haven't really been able to get into this game. (I did make it to the Underdark once, however, and no, I didn't skip Spellhold; I have never actually done a polymorph teleport.)