There are two things that the Mentor system brings to the table: the Mentor roulette, and the Novice Network. There's literally nothing else in the game that's affected by it other than a cosmetic change to your search info if you so wish. Between too many NNs being cesspits of toxin and decay, and they being a very limited chat channel to begin with whereas Mentors and Sprouts/Returners can't even get in, that leaves us with the Mentor roulette. In the patch the Mentor roulette was released, they said in the patch notes the roulette itself was specifically to help queues for those pesky duties that don't pop.
Everyone can be helpful with or without the crown. Everyone can be a piece of trash with or without the crown. "So long as a mentor has a good attitude"? Has nothing to do with them being a mentor. We're bodies to get the queues going.
Uh, #NotAllMentors much? A lot of them do. I know a few people who cheated the DF system, powered through the achiev in two weeks, and only use the mount to shove it in people's faces.Mentors don't choose to be mentors to impress you.
And all the questions you brought up aren't things you need a mentor for. It's why the Novice Network amounts to "let me google that for you". Hell, you don't even need that, most of it is information that exists inside the game. It's also information people somehow managed to grasp before the Mentor system was introduced.
Remove the Mentor system tomorrow and the only thing that'll change would be -- oops, certain queues not popping. The Novice Network is now replaced with the Limsa shout chat.