Sure you can (besides your mind)!
I can carry a knife, pistol, rifle, smoke a cigar, and sip my favorite beverage all while flying *my* plane.
What you are talking about isn't a restriction on private transportation, but on mass transit.
Well, mass transit, be it busses or aircraft (regardless of who operates them), is a lot like being in public. You don't expect to be able to run around naked in a public park, for instance, but you can run around naked inside your private house.
Same thing with aircraft. What you carry in a private aircraft is quite different than what you can carry in some form of public transportation.
So if you want to be free, use your freedom to purchase private property such as your own aircraft (they actually aren't even very expensive if you buy them used).