While I agree that TSA should be done away with, I'm afraid that it wouldn't actually change what airport security looks like in most places. At this point, since people have gotten used to it, my guess is that if Airports took over their own security again (or went back to however it worked pre-TSA), they would maintain about the same standards and procedures in an effort to avoid blame in the case that something happened. Regardless of government involvement, it is extremely hard to work back these ratchets on security theater.
On the contrary, I think airports would desperately like to do better. Airports are hated; improving the experience of airport security is extremely important to them.
I could legit see an airport in a major metro advertise "Fly through PDQ instead of SRX - you'll save an hour of your time and nobody will ask to touch your genitals"
The actual screening would probably be the same. But the customer service side of it might improve when airports can compete on how nice the experience is. I don't imagine these scanners are ever going away, but loudly clueless workers don't have to be part of the experience.
Blame/lawsuit avoidance is a powerful motivation to keep things the same. But there's also a very strong drive to reduce costs, and this would be a very enticing cost center, for better or worse.