What if you are a US citizen, and it has recently been discovered you have been secretly dealing arms to Russia against current sanctions. And while authorities do not currently know your location they suspect you will be flying to/from Russia very soon?
That's totally different - indictments are usually sealed before arrests in the kind of case you're talking about and there is longstanding precedent for that to prevent flight from prosecution. They would arrest you for ITAR and IEEPA violations before you board. That kind of thing happened long before the no fly list. That is different than an opaque list with a million people on it most of which have never been accused of anything and where there is an expensive appeals process and the government is allowed to use secret evidence.
> The No Fly List is a small subset of the U.S. government Terrorist Screening Database (also known as the terrorist watchlist) that contains the identity information of known or suspected terrorists.
The TSA comment above is pretty straight forward but to be fair the wiki article is filled with instances of speculation.
Should they let you know not to book a flight?