They depend on intimidation. A mom of three, with kids in the car, may well know that her car cannot be searched without a warrant or a specific suspicion. However will she run the risk of being abused, shouted at, guns waved around, kids scared, everyone prevented from leaving for a long time, and so on?
Tyrants always target weak and defenseless first. There are tons of examples. Hitler started his euthanasia projects with killing psychiatric patients - and there was a large ad campaign about how much it costs to feed them and how little is gained. Of course he then switched to other categories of people.
In the USA your local tyrant will threaten you with layoffs in your town's police and fire departments unless you cough up additional taxes. The meme "for the children" is universally used to push any evil agenda through.
In this case an unprepared traveler is caught in a carefully prepared dragnet. There are armed people all around, there are vehicles, communication, support - all that against you personally, who has none of that. You are massively overpowered; even if they let you go it's not because you told them to get lost - it's because they decided to let you go. There is a huge difference. Your rights are violated the moment they attempt to stop you.
The TSA have become the terrorists.