Even if the game is not designed to use that system, couldn't they try to change it?
What if they added a new command called "march" that would make your units walk slower to not lose/recover stamina? This would give the player a lot more control of his units stamina.
By the way, I'm not really a big fan of reducing the amount of arrows the horses archers have(assuming that it's not extremely high). And making horses more fragile? That sounds bad to me. I know this is one of those cases of realism x gameplay, but horses should be difficult to kill(in my opinion). The other options of balancing cavalry are fine to me, moreover, the devs don't need to use only one or two of those options, they could use the stamina system+make horse archers less accurate+reduce the penetration power of cavalry against infantry, or any other combination that they want.