The Christian Hell mythology is contradictory because it’s almost entirely fanfiction, and a much more modern fanfiction than you’d think, particularly in regards to Satan’s role.

The long and short of it is that, if you assume the Bible is an authority on such things, Hell isn’t this major thing where most people end up because they didn’t believe correctly, it’s not a physical thing at all, much less a thing populated by torturing demons, and Satan wouldn’t be in charge, or the Warden, or anything like that. He’d be a prisoner too.

Even in Inferno, Dante depicts him as imprisoned in ice.