You don't have unfettered ability to come up with a personality and backstory, though..
@Oofta says no evil characters. I allow evil characters, but require your evil characters to find some reason why they get along with the other PCs and aren't going to sabotage the campaign through evilness. Further, if you came to me with a backstory that you met a hermit that was a gold dragon in disguise, I am within my rights to say, "You can have a hermit in your backstory, but he wasn't a dragon."
I also have the ability to go into your backstory and bring elements of it forward into the current game, which most players find to be an amazing thing that DM's do. That hermit might show up for X reason.
Character creation is not 100% the players doing and as such the resulting character is not 100% the player's.