I would just let the airlines pick if they want TSA screening or not. Customers could buy flights with whatever security level they want.

If you fly intrastate in Alaska there is no screening on commercial flights (it seems TSA must not be required on non-interstate flights). Technically it's still illegal to bring a gun but no one would know one way or the other. It really didn't bother me that there was no security, in fact, it felt great, and at least I could be sure if a bear met us on the tarmac someone would probably be ready.

I know of one other story I heard secondhand from someone experiencing it, of a small regional airline in the South, where if you checked a gun, the pilot just gives it back to the passenger...