they often argue that allowing something in one state, even limited to that state, impacts commerce in other states. I think they would use a similar argument here.
If there is such a topic or situation, we can always fall back to the "national security" rationale. That covers everything else the federal government wants to impose on states.
Congress is allowed to make laws (covered by the constitution) if that law grants the federal government the authority over something then the law is covered by the constitution.
It's perfectly reasonable to want one set of rules instead of a patchwork across very open borders. But just saying "you can't do it" is pretty lame compared to actually coming up with sensible rules first.
My understanding is that courts usually require actual constitutional federal regulations to exist for Federal Supremecy to apply. But this is just cooercive regulation through barely related funding. I believe that's generally legally acceptable.