I don't think your comparison with Cthulhu Dark is appropriate. You've got it backwards. It's not like the PCs chose longshoreman, legal secretary, etc. in order to get specific bonuses. That would be an appropriate comparison if the Paladin player had said, "Hey, I love the whole thing about the Oath and stuff, but I don't want all the Paladin powers. Can I just be a 0-level commoner who has this really strict Oath?"
If the player had said, "The whole Oath thing doesn't float my boat, but how about...." and proceeded to offer a totally different story from the one offered in the PHB, that would be ok, too. But the example wasn't given that way. It sounded like the (imaginary) player just wanted to have the cool buttons to mash with no story around it.
And to be clear, I don't think there's a balance issue with that at all. It's not that I think the Paladin is overpowered and needs to be reined in via Oaths and roleplaying. It's just that when I imagine somebody wanting to discard the inconvenient bits, with nothing offered in its place, I assume (perhaps unfairly) that he/she is being a pure powergamer with no interest in storytelling.