OK here’s my crazy Supernatural fan theory that won’t be true but I’ve put thought into and can defend like a college dissertation.
I don’t think Naomi is an angel.
I think Naomi is a pagan minor god or the former minion of one (well probably former though not necessarily).
I think, possibly as early as season 6 but likely during season 7, she got a hold of an angel and poked and prodded at it but unlike Crowley wasn’t under time constraints.
I think she’s working at making the angels her own army and supplanting the god figure head and gaining… whatever human souls energy blah blah whatever heaven and earth offers supernatural beings.
I think that’s why she was able to send angels into purgatory and retrieve Castiel - since she isn’t actually part of the Christian mythos, she was able to make a door. (Though it might also have been her own cronies and not other angels at all - kinda besides the point since I’m sure the show will never give an explanation anyways so who cares).
I think she brought Castiel out of purgatory because of his connection to the original creator of the angels (his constant resurrections) and possibly fear that he’d show up at an inconvenient time and overthrow her. As is his habit.
Bad guys do like to keep their weaknesses close at hand, after all, though I don’t know if Castiel would hold any particular power and it isn’t just “your reputation proceeds you” stuff. Possibly why she ordered the Winchesters to be watched, although that could also just be because of knowledge that it is a mission that would distract Castiel himself.
Anyways. She specifically told Castiel he can’t go to heaven. Why?
Because she doesn’t want Castiel to see what heaven has become or she doesn’t want other angels to see Castiel?
It’s either she’s only doing torture on a select few angels (like Castiel) and other angels would be able to tell (doesn’t really fit my theory, just wondering what’s up Supernatural in general) or she’s afraid Castiel could break some programming of other angels (possibly see Hester, but admittedly this is probably not true - but possibly was something she feared before getting heavily into controlling Castiel) or she’s already reorganized heaven and isn’t confident about her programming of Castiel yet or just isn’t finished (probably it has to be done in stages) and seeing heaven would break or set back what she’s done so far on Castiel.
Samandriel didn’t want to go back to heaven either. Control, Naomi, etc.
Heck, maybe Naomi already has the angel tablet or knows what it says, maybe it says how to control angels?
Which (sorta) leads into :
SECOND CRAZY FAN THEORY
The angel tablet doesn’t seal heaven.
It’s a kama sutra, a sex manual for the angels! Create babies! Includes a recipe for a “sex bomb”! xP
Nothing says it really has to be the exact same thing as the demon one!
(And Naomi only said “if the demon tablet can … what do you think the angel tablet can do?” Nothing said about it being the exact same thing! I can compare apples and oranges too, that doesn’t mean they taste the same.)