I think the biggest problem with carts is usually when you have too many wounded men and can't get out of a region, you just stay scattered to heal your men back up. You don't try to use carts to get out when over half of your men are wounded. It just feels cart's role is filled better by healers. Sure healers cost a bit more but even 2~3 healers are better than 1~2 carts in most cases.
