Sorry, this is unrelated and i'll go on some autismo rant: Let me try to think this backwards. Why do you need "legal permission" to go to earth? I cannot find a real reason, only fanon excuses. That implies you need certain qualification but Blitzo sure as hell has zero and this would not be a secret. There is no way the police doesn't know he went to earth and killed people. So it it can't be "interfering too much with earth upsets heaven/lucifer" (another fanon). But it that's "legal" then what could possibly be "illegal"?
Honestly, the core issue is that in HB Hell is too separated off from Heaven, and in doing that, they made rules and regulations make no sense. Going to get a little spergy, but if they had one guy well versed in even the Old Testimate, the answer would be simple, the demons that are legally allowed to go to earth are the Jewish rendition of “satan” as seen in the Book of job, and have/need express permission from Heaven/God to spread sin and tempt humans. This can serve Two Purposes.
1: Since Heaven is involved, you now have an excuse to temper what your characters can and can’t do. Sure Succubi can seduce humans, but they can’t use lust powers on them, it must be consensual, and oh look, your gooner bait race is now less problematic. Infesters can posses humans, but they can only whisper to them and implant ideas, the human must act on that idea themselves. You can show how they manipulate humans, but when they fight other demons, oh look, they were actually holding back and now IMP are in a fight of their lives.
2: it adds a reason that BLitzo needs an unregulated book, Heaven focuses on the masses, and him going through legal channels will bring him face to face with the Heavenly Host, and even if he lies about why he needs it, they will know when the crystal or other means to reach earth is used, and IMP will then have eyes on them at all times making sure their approved mission statement is not violated. However, someone like Stolas is a non-entity. Powerful? Relatively speaking, yes. But what’s he going to do with access to the mortal realm aside from his farce that the Goetia call duties? Whine on reddit about his wife and how gay and sad he is and get karma? Join some Role Play server on Discord and live out a gay fantasy he can jack it to afterwards? He might go to some furry convention. Oh no. The book is a blind spot, and that’s what just what Blitzo needs. Hell, the sins, even the devil himself won’t care he’s killing humans, because they despise humans, why would it come up in a trial? But Heaven would care. And if the angels found out, issues would arise and consequences would be certain. (How many of us would pay for an animation were one angle beats the ever loving snot out of Stolas and/or IMP for the crap they pulled)
Issue? This is something I pulled out of my ass this morning a minute after reading this comment. Bigger issue? This requires Heaven to be good and hell to be bad. It requires an actual knowledge of scripture and theology and bending it just enough without it snapping. In trying to be the edgy pre-teen what if heaven bad hell good, but still keeping hell as hell because HH is about redemption, you can see that the world building is twisted into this gordian knot of terrible world building and writing.
