There's a Snail Speed in the Rise of Mankind mod (over 3000 turns). I don't think I could bear it.

How is the balance badly effected?
I'm trying to think of how you could reasonably do it. Do you suggest the movement for foot/mounted units should be something like
Quick = 3/5
Normal = 2/4
Epic = 2/3
Marthon = 1/2
Even if they could achieve scaling the unit movement with game speed, wouldn't it pretty much remove all difference between the speeds besides the actual length of the game? I guess this is what you'd like, but personally I wouldn't have played Epic, let alone Marathon, if it only meant finishing a game would take way longer.
Well, I'm not sure how to answer this response. At the beginning you ask how the balance is affected, but then at the end your argument seems to be that it *should* be.
Personally, I'd prefer the game to go quicker. However, it's pretty frustrating to war on normal and just about impossible to do it effectively on higher levels with quick. Giving units extra moves would create balance problems too however - like instant city captures from outside culture borders (which usually takes planning or weak culture). The other problem is scaling which your suggested movespeed changes indicates - epic is 1.5 times slower than normal but civ might have difficulty with that...but rounding is problematic - in your suggestion mounted gets NERFED TO HELL on quick and epic.
I don't know if there's a good solution to this other than just to stay away from normal somewhat and especially quick (a game speed that's so broken that almost nobody on this forum voted that they play it).
Anyway, in case you still aren't aware of how balance is badly affected:
- On a speed like quick, it is literally possible to mass an army as an army that declares marches to a city. For every city it tries to take. Hello WW, good-bye fast wars, even with a lot of prep. It allows one to shirk military more and get away with it.
- On faster speeds, it is possible to be declared on, not have gunpowder, lose 8 of 14 cities across 30ish turns, and still have self-teched rifling and produce some rifles (ending the war because in this case I was using drafted janissaries and rifles screw them). THERE WERE NO TECH TRADES - I made sure of this very carefully...

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- Combining a high difficulty with quick means a unit a turn or very close in many AI cities. This is extremely imbalanced in favor of the AI since basically they pay a tiny % of what a human does to upgrade their army.
Production speeds, healing speeds, peace treaty duration...none of these things scale! On marathon unit costs don't even scale! Each difficulty is like a different game. Some people say that Epic/Marathon are easier and it's probably true - but I also kind of like the fact that if you don't have a military and you're declared on, you're toast. That feels a lot more realistic then suddenly conjuring up magical forces of 15 rifles by the time the attack stack reaches the 2nd city without drafting, honestly.
If I could stand marathon's slowness I'd play it.