Lilith, Rosie, and Alistor Theory
MINOR SPOILERS FOR SEASONS ONE AND TWO
Recently, I rewatched the entirety of Hazbin Hotel, and there were a few details that stuck to me on a second watchthrough; particularly the scene prior to Alistor and Rosie's Don't You Forget musical number.
It's my theory that Rosie -- when alive -- was a powerful witch and a women's suffragist. Given the Americana trappings of her town, it would fit with the time period. I'm willing to bet she used black magic to protect women and to ensure that women were given the right to vote in America. Rosie undoubtedly also ate the men who stood in the way of her political goals or dared to abuse other women since husbands abusing by their husbands were all too common during her time.
This is why I believe Rosie was best friends with Lilith, connecting over the fact they were both outspoken advocates who refused to blindly obey the whims of men.
Furthermore, I believe the reason Alistor went "off the air" around the same time Lilith first disappeared is because Rosie (S2 Spoiler) >!sent her most capable "pet"!< to go find her, and that it took Alistor seven years to discover something that allowed him to come back home. Something that made Rosie concerned enough send Alistor to go help Charlie with the Hazbin Hotel as its "host". Though I believe it to be nothing more than a pretense to cover up his actual assignment of protecting Charlie. After all, who better to play bodyguard than the most powerful Sinner in all of Hell?
Protect Charlie from what? I don't know. It couldn't have been from Adam since her, Lucifer, and all hellborns were exempt from the Exterminations. Plus, the deal would've been made null and void (S1 Spoiler) >!when Adam attacked Charlie!<. And going by (S1 Spoiler)>!Lute's dialogue at the end of the first season, it seems like Lilith was the one to reach out to Adam (or possibly Sera)!<, and not the other way around.
There's also the little caveat that there was (S2 Spoiler) >!an intended exit clause to Rose's soul contract with Alistor by him completing some unnamed task!<. Unfortuntely for her (and perhaps Charlie/Lilith), (S2 Spoiler)>!Alistor exploited the loophole to break free out of his binding obligations!<.
As to what that task was or what Rosie was so worried about that she felt it necessary to send the Radio Demon as Charlie's protector, I have no idea. There simply aren't enough available clues to piece that together right now. I suspect there's a hidden player that won't be revealed until season three, but we shall see. Whatever is on the horizon though, it's enough to keep Alistor around the Hazbin Hotel, and I suspect it has to do with Lucifer based on how the final scenes with them were shot.
Perhaps Alistor will become the antagonist in the next or later season with him attempting to take over Hell? Alistor does now know that (S2 Spoiler)>!Lucifer can't smite Sinners!<. Though him attempting a takeover seems unlikely. Alistor's not like Vox who seeks to seize dominion or anything like that.
As a side theory (more speculation), I do believe Alistor did manage to track Lilith down in (S1 Spoiler) >!Eden and/or Heaven. Lilith is always seen having her cellphone on hand, and even modern phones tap into radio waves for many things.!< Obviously, the Radio Demon can also tap into them as well. (S1 Spoiler) >!I even suspect that Alistor was able to contact Lilith through her phone, even though he couldn't reach Lilith physically.!<