The idea with stamina would be to alleviate the problem that you basically can play the whole game with one or two survivors instead of all four. Also, it might help to counter the “over-specialization problem”, where one player is always fighting at the front while one is forced to plant watering service.
Basically, after a while of fighting or carrying heavy equipment, the survivor gets tired and can’t perform those heavy duties efficiently any more and you have to switch through and use another one on the front line.
It also opens up a new game design space for playing with this stamina attribute (enemies draining that stamina; items that replenish it; etc.)
But I also see your point of adding another layer of management, which might make the whole thing more bulky rather than more elegant. I’m not sure about it; maybe we gotta test it.