A State should, right up until it starts infringing on our Rights. The Bill of Rights applies to all US Citizens living in US Controlled territory. Regardless of "home rule" cities or State "powers".
By putting this issue under the federal umbrella, do you think further increasing of rights is likely, or less likely?
The Constitutions of the Several States applies to RTKBA..for that state, as the DC v Heller case showed, States may impose reasonable limits on the State, but cannot outright deny the RTKBA.
By expanding the scope of the FedGov one is merely opening the door to yet more restrictions, though I doubt one realizes it.