Why do demons and devils want souls?

[Jalouis]

If you follow on from Wraith: The Oblivion, then souls are what are smelted down into relics and the only currency of tangible worth to the society of the dead. Symbolically, they can be seen as the memories of life that can fetter a dead soul from slipping into oblivion.

[Varyon]

Originally Posted by BeckJohn21

Demons are basically just masses of raw elemental energy, given form when they're summoned by mortal sorcerers. Once the summoning ends, they begin to dissolve back into the chaotic energy they're made from. Some demons are content to return to nothingness, but others desperately want to continue to exist, which they accomplish by binding human souls into themselves. The souls continue to perceive them as discrete beings distinct from their environment, helping them maintain their shape and individuality.

I like this concept. It reminds me a bit of the premise behind the webcomic Indefensible Positions, where the daemons were basically all just figments of human imagination, but became more powerful the more fervently people believed in them (and the more people who did so). Sometimes daemons could even get in on the effect - two of the characters in it are indicated to continue to exist beyond the point they should have dissipated (one was the imaginary friend from the childhood of a college student, essentially resurrected and empowered by a powerful sorcerer to disrupt the ritual of an enemy by taking the place of the intended sacrifice; the other was the memory/idea of a recently-deceased soldier as recalled to his child he never met by his widow, summoned and bound into a robotic body to serve as a protector) essentially because they each believed in each other. In the case of your example, you've got the interesting effect of a demon continuing to exist because of the disembodied souls it has bound to perceive it, while said souls only persist (rather than moving on - to an afterlife, to rejoin the river of souls, or whatever) because they've been bound to the demon.