As the title says, why don't illithids have souls?

Isn't there an illithid god named Ilsensine? I mean, I don't wanna get lost in lore, just curious.

Also, if illithids don't have souls... and that's why the other gods and Jergal are concerned... why are the dead three getting rid of souls? How does that help the dead three who, at least I would imagine, rely on souls themselves for their own power?

I feel like there's an aspect of the illithids not having souls that I'm missing.