If Brady can design an offense to get the most out of QB, then he should be able to have success doing that with Carr just as much or more than with Rattler. If a new coach brings in a new offensive system, then both Carr, Haener and Rattler would all be learning a new system, so none of them have an advantage over the others regarding that.
People are grasping at rationalizes for why the QB they prefer would be the best choice for a new coach. There's a lot of QB wish casting going on, which is not at all unusual.