I remember suspecting that my Mom's recovery had to do with them giving her an "out"....blame it on the demons rather than your own weakness or immaturity. As kids, we didn't care so long as she back on her feet again.
To be fair, that is one psychological benefit to the belief in exorcisable demons, it has been so observed.
If you can think of a psychological hangup in this primal, mythical way and see it as an imp or a thing that can be removed from yourself, you might well feel better once it's gone. That's partly why Mandaeans love baptisms so much.