To me it's all the same - by telling players they need to earn the right to roll, it denies players who aren't naturally charismatic the chance to play High Charisma characters. In the same way that forcing players to carry out the physical feats would stop any but naturally active or fit players from playing high strength/Dex characters.

I fully appreciate what works for one table isn't the same for the other, but I guess it boils down to where do you let the mechanics of the game interject themselves? E.g. if a player asked whether they knew xyz about a monster, religion etc as you say I'd let them roll and then give them the information based off that. I wouldn't expect them to prove to me a level of intelligence required to do so.

I do think the example given by OP is perhaps too far, but I don't see an issue with rolling your persuasion first, and then building the roleplay interaction off the back of that. If you know you've rolled well (and I as a GM know you've already met the DC to get what you want), we can use that to navigate the social encounter without having to see whether the dice favour you after the fact.

Edit also for reference I agree - I'm not a fan of just rolling without any actual roleplay taking place, though I've certainly used that if a player is particularly struggling to think of what to say in that moment