It has nothing to do with our form of government. It has to do with State's rights vs Federal rights/law. If the Federal Government gives me the right to fly, why should I agree to let the States take it away or limit that right?
Well, because you're a decent person, respect the wishes of others as being equally important as your own in public places, and are willing to negotiate and compromise so everyone has a chance to meet their needs.
Or not. I'm not allowed to describe what most of us fellow citizens think about the "or nots". The vocabulary is prohibited on this site. Also, the "or nots" tend to provoke anger, escalation, and too often violence.
It's very similar to having a loud party, not quite violating the local sound level ordinance, but irritating your neighbors nonetheless. When they knock on your door, you get all, "I know my rights!" with them, and they walk away mad. This is the stuff neighborhood tragedies are born from.
Instead, had you visited you neighbors a few days ahead, let them know about the party and that it may be noisy for 5 or 6 hours, I guarantee it will come out differently. Perhaps a neighbor has to get up at 4am, and asks if you could quiet down by 11pm. You agree... compromise.
"why should I agree to let the States take it away or limit that right"?
Because sometimes it's the right thing to do.