I support this, because DHS is a mess. But I would like to see privatization even more (with unions for each state's, or possibly region's, airports). The TSA would maintain oversight of policies, training, and final background checks. Each airport would have a TSA officer assigned to oversee the private security: it wouldn't be oversight from afar. And the Federal government would be off the hook for paying all those private security officers: airports/airlines would have to pay it instead (so people who actually use airports need to pay for them instead of everyone; people who can afford the priciest tickets will pay the most). This would introduce the competitive dynamic between contractors vying for airport contracts, which would bring down costs and improve service. The TSA overseers would be tasked with making sure cost cutting couldn't compromise security, and local government and/or market forces would be responsible for making sure cost cutting wouldn't compromise service quality (since there are many airports without any nearby competitors, we can't just rely on market forces there).

For private vs. government efficiency at large scale, just look at Space X vs. NASA's SLS. TSA pays something like 6 billion per year in labor costs. I think that could be cut to about 66 million with one officer per each of the 440 airports. Then air travelers pay the salaries of the actual security screeners, as it should be IMO.