I don't think this argument really works, because you can also classically simulate superposed states as long as they are stabilizer states, or fermionic gaussian states, or log-space states or whatever else. Similarly you can also classically simulate states with arbitrarily large amounts of stabilzer magic if they happen to be fermionic gaussian states or whatever.

I think you can sort-make the argument you want to make, because all computational basis states are also product states, just like all computational basis states are also stabilizer states and also (if they have the right parity) fermionic gaussian states. Where it goes wrong is when you start thinking about gates/circuits instead of states, because (e.g.) CX or CCC..CX gates with arbitrary numbers of controls are (in general) highly entangling gates, but they map computational basis states to other computational basis states.

Does this make sense?