Link
So I've reposted this awesome post a few times, and it only recently occurred to me that hey, what exactly are the implications of Alastor doing this?
The gist of the post is that, in Hell's Greatest Dad, Alastor adopts moves Vox uses in "Stayed Gone". He's a talk show host, a religious figure, and he crowds around Charlie in multiples.
I will add on re-watching it that he also re-colors his own suit from red to blue, frames, as this post pointed out, an inner world very much like the Vees', and heck he even busts out the piano, which the Sparks print implies he used to play with Vox.
But why? Is it just that he's always got Vox on the brain? Maybe true, but in context, what is Alastor doing in this song? He's trying to frame his relationship with Charlie as familial. He's hoping to piss off Lucifer by pretending to be a father figure to his daughter. And where does his mind go when he's trying to simulate family, to imagine being affectionate and close to someone?
To Vox.
Because in Alastor's mind, that's what he knows of family in hell.