One of the "Problems" with this proposal is how it will interact with "time limited" battles. I believe that currently battles go to a "draw" if it lasts too many turns, or too long in general. I haven't seen this recently, but I could have sworn I saw it once long ago.
If we implement limits on the amount of fighting that can happen each turn, it is very possible that battles simply never get resolved. If you have 3000 men vs 3000 men in a location with a line width of 250, you'd never finish the battle. It would take ages upon ages to finish. Granted, this helps archers, but it still wouldn't work out very well in general under those circumstances.
Just something that needs consideration.