I think that's the trap a lot of people fall into, that a position needs to function in a certain way or cover a definitive role - the game is in constant evolution with coaches always trying to figure out how to outsmart the opposition, the one rule of thumb is "always play to the strengths."
Unfortunately we don't have a playmaking Fullback who is ready other than Mbye's potential and history in juniors.
As for the argument of Coote, I would simply say the likes of Tedesco, Munster, RTS, Inglis, Stewart and Slater are run first, pass second Fullbacks.