The problem is, the class list does exist.
I agree that I hate gameplay where BD can just skim the class list and check off possibilities until the evils have nowhere left to hide. But it’s even worse to have a hidden class list that only vets know, since that makes the game harder to learn and gives older players an unfair advantage. A game like ToL is already hugely complicated, so we should try to make learning it as painless as we can by having the game be honest and upfront about the mechanics.
I’d be all for loosening the class list in any way that people feel wouldn’t break the game. But to the extent that it does exist, the game has to tell players about it.
(That said, it’s true that the “physician / alchemist” and “3 neutrals max” rules are hard to convey. Also, the game needs to more prominently tell people that there’s at most 2 of each class - that is far more important than the Phys / Alch requirement or even the Sheriff / Paladin requirement; it comes up almost every game. Yet right now it’s sort of hidden and hard to find.)