"The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized."
One might say that you submit to this as part of the deal to get on the plane. But if that were true, it would be between you and the airline, not the government. That means it really should be the airlines that decide how intrusive searches should be. And you would be free to choose an airline whose policies you agree with. And the airline would be free to reject you as a passenger.
The government has hijacked the relationship between you and the people you've hired to get you from point A to point B. Just because of previous lapses in their intelligence efforts enabled some people to do something terrible doesn't mean you lose your rights.