P.S. I know "the freedom of speech" is specifically referring to a compact between individuals and society, based on the writings of Locke and Blackstone among others, a "deal" that society would protect the freedom of individuals to state that which they believed to be true based on evidence and reason, and that individuals in return would only state that which they had reason to believe to be true and which protected the life, liberty, and property of others--that is why libel and slander are not protected by the First Amendment. Nevertheless, the Fourth Amendment protection is against "unreasonable search and seizure," while the First Amendment protection is much closer to absolute, as close as possible without turning the Constitution into a suicide pact.
What does not infringe mean?
There is nothing reasonable about the TSA or anything it does.
Good analysis and your thinking, I believe, would shut down major portions of the Patriot Act (misnamed), the NSA domestic spying, and eliminate the TSA.