They drop trivial amounts of souls which are used to buy levels, but souls are also gained by beating bosses and from using items that also grant souls.

I've experimented a lot with this. If you just fight bosses and use boss soul items and other easy to reach soul items, you will end each game roughly 5 levels below someone who is more meticulous and clears each zone of enemies without grinding them repeatedly.

At the end of the game, those 5 levels will be a trivial difference.