Imo the main problem of Inquisitor/Sorcerer isn’t that they are poorly balanced ( which they are ), but that they produce no fun gameplay, while many neutral classes do. When I say no fun gameplay, I primarily mean the classes themselves don’t have many “choices” to make, and their presence in game doesn’t produce choice based gameplay for other players either.
As an Inquisitor, you only out yourself once asked, and then most people would believe you unless they were possessed/reaped, which is pretty easy to figure out. It’s simply a good claim to make, especially in unseen games. You sit back and play as BD until sorc is executed, which is from my experience relatively fast.
As a Sorcerer … your claim is … with every king being able to see the faction, I’m going to say - good luck with claiming. You can try claiming Inquisitor yourself and die to the real Inquisitor the following night? You can’t jump once your cover has been blown or silence people in court. You are simply a really weak NK who is killing people hoping for the best. You can try claiming Alchemist of course, but that’s not very compelling, any neutral can do that and maybe live another day. Having NK’s main go-to claim be the Alchemist is what created the whole “Neuts Out” meme anyway.
Another problem is that Inquisitor remains a kingmaker after he wins. Scorned already has this side effect where he is left as a player in game with no goal after they have won.
My suggestions? Give the sorcerer the ability to affect the court somehow. Improve their subversion ability. Let them hide, switch positions with a player somehow, maybe with the inquisitor for one day - anything, allow them to mix up things. framing people as magic users is not good enough. Maybe they can make players appear as neutral/immune for the night? It could somewhat demotivate rapid neutral lynching. Or make it so Inquisitor can be converted after he loses his shield. Just throwing feelers out here.