Golden Horde!

[drone]

Staying power is used to let the Arbalesters empty their quivers, right?

Not necessarily, though it's nice. You need units that can hold the line, not take too many casualties, and can recover from fatigue. They need to be able to stand in for at least 2-3 waves. The Arbalests will work through their quivers regardless, as long as they get protection.

I guess this indeed comes down to playstyle then... First of all I hate long drawn-out battles and avoid them in the first place, and secondly, perhaps as a result of that I often find myself incapable of using Arbalesters on less than mountainous terrain.

This is true, if you find something that matches your play style and works, great. I find myself incapable of controlling large numbers of archers, and can't use HA to save my life. So I get around it by using different tactics.

Well... Once again, which unit do you have in mind that doesn't?

Chivalric or Feudal(w/ armor upgrades) Sergeants or Armoured Spearmen on the lines. It's not sexy, but they will retain their numbers and energy levels longer, thus maintaining morale.