I think you underestimate the piety of the medieval world. Except for the Normans. They were totally in it for the lands.
But yeah, in small wars between counts and stuff you'd be less likely to keep a train of merchants simply because you'd travel a few dozen miles, commandeer peoples houses and food, bring a bit of your own, maybe hunt if you're lucky, then fight. Or you'd already be looting since thats what most war boiled down to. In wars between kingdoms you'd be a lot more likely to work with merchants than to loot them simply because a large concentration of men and horses can very quickly eat everything in a small area.
And realistically, you don't burn down the fields and uproot orchards in lands you hope to annex.
Widespread looting to support "armies" is actually more common in and after the Hundred Years War than before it. Prior to that, the "classic" example of looting is the Vikings... who weren't supporting vast armies in most cases. The wars between Wessex and the Vikings of the Danelaw might provide some good material concerning looting to support armies, but, if it exists, I am ignorant of it.
Of course, this discussion may hinge around a definition of "looting" as opposed to "taxation."
