And I don't see any problem with specific unit settings for every game mode.
If you're suggesting there should be different settings/mechanics for different game modes, this was suggested in beta more than a year ago, but the developers themselves said they "can not split the game mechanics for different game modes" for whatever reason:
So unfortunately we have to consider the mechanics as universal for all game modes.
Archers can't run and shoot at the same time, you know that right ?
They can jump away and shoot at the same time. Not the bots, but real players. After the 1.5 update, it's now less feasible for them to keep on doing this. If they were able to run faster, the advanced players out there would probably be able to run and shoot and keep the same distance, especially since the chasing infantry would have to bring up their shield when they shoot, which slows you down.
But it's also enormously unfun, say in TDM, if you hold your shield up at an archer firing at you, close the distance, go to attack, and then he just runs away (even if he doesn't fire back at you periodically, which with faster foot speed, he would). It's a similar deal to Horse Archers, which were banned in popular Warband servers, just because of how toxic and anti-fun they were to play against. And at least Horse Archers were specific to one faction, so they weren't as widespread as archers. With archers on foot, they definitely shouldn't have that ability that Horse Archers have of simply moving away from infantry if they get near. Not because of realism, but because of a consideration of what's fun to play overall.
As for dealing with archers in Captains mode, I would send cavalry to deal with archers. This is nothing new, since this kind of strategy (and much more) has already been part of Warband for over a decade. It's very elementary and easy to understand. But if the archers were so poorly positioned that infantry actually managed to catch up with them, that should be the archers done for, unless they get help from other units. Other things can improve about archers, but their foot speed right now is reasonable.
And I want to make clear that I'm against increasing the foot speed of archers specifically. I'm open to the idea of reducing the speed of shock infantry. They could definitely do with a significant nerf.