Exactly. If a private security company wanted to require pat downs outside their airport, they could. But I doubt the airlines would hire such a company given the public outrage it would create. The TSA is a federal agency. Like you said, it cannot do whatever it wants and tell people to deal with it. If that were the case, we might as well burn the constitution now.
they could hire a private company, but if they don't search in the same was as TSA, no flights would be allowed in or out of the given airport.
and the 14th amendment doesn't prohibit searches. it prohibits UNREASONABLE searches.
you're not one of those idiots who only wants arab-looking types searched, are you?