I'd say AI of Sovereigns just stinks in general.  If they would spend less time smashing their faces against my walls and more time just walking around their own territory looting abandoned lairs, they'd be a lot happier.

I'm pretty sure this is what happens when they clear lairs with troops (their heroes are all off doing something else). It's somewhat understandable, they have other things in queue to do, and they can buy equips, so picking up loot is lower priority.

Normally AI heroes are pretty good at picking up loot, sometimes they'll steal yours if you kill a lair and don't have the movement to loot.