If the players would be willing to trust the DM, and not argue with him about where their characters are (even if the DM is incorrect in his assessment of where their characters are) then a big fight like the Balin's Tomb Fight (that's what I'll call it

) could take place at high speed.
Would it be totally accurate? No. Might it be unfair to the players from time to time? Yes. (But then, it would be unfair to the monsters too.)
But would the characters themselves know exactly where they were, at every moment, during a Balin's Tomb fight? No. (humor:

Well, I am, on second 3 of round 6, at 22 feet from the entry, 14 feet from the tomb, 5 feet from the raised walkway, 8 feet from pillar 1, 15 feet from pillar 2, and of course I take the time to look around and confirm all this. The fact that 5 orcs are attacking me and the room is filled with combatants, a cave troll, and a huge amount of dust ... not to mention the lighting is lousy, makes absolutely no difference!

)
ThoughtfulOwl, that may be a Tidbit, but it makes a BIG difference!
Cute Elven Mage (5th level wizard) wins initiative (high Dexterity, Improved Initiative) against the 5th Level Fighter with his full plate armor and large steel shield.
Cute Elven Mage is Casting on the Defensive. Makes DC check of 16, readies Shocking Grasp.
She attempts Touch Attack against Fighter, hits, does 18 points of damage.
5th level fighter decides to run. Takes Double Move, moves 40 feet.
Round ends.
Mage casts second Shocking Grasp, holds charge. Mage moves 25 feet after running Fighter.
Fighter decides running was bad idea, turns around. Can't take 5 foot step and make Full Attack (mage is 15 feet away), decides to take move action and make one attack. Does so, hits with axe, does 5 with axe + 4 for strength + 3 for enhancement for 12 points. Mage survives attack (she had no constitution bonus to hit points, had 14 hit points at start.)
Mage does not need to make a Concentration Check to Hold a Charge.
Mage delivers Touch Attack against fighter, hits, does another 18 points of damage with Shocking Grasp. Fighter has taken 46 points of damage, is at - 4.
Cute Elven Mage delivers Coup de Grace against downed fighter.
Ok, the move of 25 feet was a tactical move, suggestion a board game.
Yet ...
The elven mage could have appreciated the danger of just running right into the fighter, when he was clearly halting his run and preparing a devastating counterattack. So, she halted, just out of range, taunting him, holding her Shocking Grasp. That would be tactical roleplaying, not tactical wargaming.
What do you think?
EDIT: In 2nd Edition, fighter just stands there sneering. Mage can't possibly hope to hit (needs a natural 20.) Fighter doesn't even attack, just stands there and laughs. Remember that fighter gets no penalty to movement for armor class, due to his great strength, in 2E. So he can run and otherwise move just as adroitly as the elven mage can.
Then fighter attacks with weapon in both hands (with high dexterity, almost no penalty at all), and downs mage (who is AC 10, or at absolute best AC 14, because she has no access to Feats that increase Armor Class.)
For that matter, mage probably doesn't go first. She has no access to Feats like improved initiative. If she tries a spell of any sort, fighter just whacks her across the face (1 hit point of damage) and disrupts spell.
After downing mage, fighter beats on chest, declares himself Mr. Big and Bad, uses heal NPC on mage, takes Cute Elven Mage away as slave.