If background checks are considered legitimate, I don't think it is unreasonable that a state issuing a license to carry also searches its own records, not just NICS. But to me, that is the rub. A license to carry with a "deep background check" should also be a license to purchase. You show your license, the seller checks with the state that your license is legit and hasn't been revoked, here is your firearm, have a nice day and enjoy!
That's how it works in a number of states. If you have a LTC, there is no NICS check. Handguns are cash&carry and that was really bad. And with 'really bad' I mean bad for my wallet. My LGS knew that and there was always something 'he had just got in....'.