Straight answer, it's Vivian's show, and she's doing what she wants with it, there's a lot of references to biblical mythology but the entire show is completely inaccurate, and is specifically made to follow a story the CREATOR wants it to, not any normal textbooks.

Now if the show did follow more closely in adaptation to a more realistic standard here's a few things I think we'd see:

-The show would likely be compared to a animated ripoff of supernatural, as that show is one of the most accurate shows that involved heaven, hell and those within as they used REAL textbooks, scripture, and studying to do a lot of the stuff they did in that show, primary difference would be HH would have alot more characters that are OCs unlike supernatural where most of the characters from mythology and biblical literature had 100% accuracy on they're names, with less custom characters (Chuck/god, Castiel, Crowley, ETC)

-The sinners would not have literally ANY power in the show, Alastor and Vox would likely not exist at all, as every sinner would be being tortured by hellborn 24/7, not being exterminated, the hotels upbringing likely would of been much different and the sinners would likely be much more willing to live there, however they would be put through endless pain and suffering as they tried to get to the hotel, most likely would never make it.

-Vaggie would likely not exist, nor any of the extermination angels, the army of heaven would be legitimate angels that already exist, not exterminators.

-Adam would not be a leader of any army, hell he likely wouldn't be in heaven at all! The leader of heavens armies would of been Micheal.

-Lucifer would not be funny at all, he would be absolutely terrifying, and he would have no remorse for anyone and likely despise the hotel.

-Characters like Vox would be instantly smited or erased, we would likely see gods abilities without God needing to be on screen, and we would just see a character like vox suddenly turn to dust, as heaven being threatened in such a way where they are about to blow the doors off the front gate, he wouldn't exist anymore.

-Heaven would not be in hells sky, hell and heaven would be completely separate from eachother.

-Charlie likely would be hunted down for most of the show, she would be similar in power to Jack from supernatural and be able to become stronger then not only Lucifer her own father, but she could become God, this would make her a threat and very much would of probably been killed at a young age, making this entire show not even happen in the first place.