How much do you think bringing a lawsuit and proving your innocence will cost in money and time? My guess is $50,000 and several years at least. The time and resources required on the government side to investigate and adjudicate what would likely be thousands of challenges would swamp the judicial system (That’s a big reason why the no fly list is secret). What would prevent the government from putting you back on the list immediately after you won your case? Most people will not have the resources to fight it.
The proclaimed guilty until proven innocent concept violates the Constitutional rights of US citizens.
If you think they're wrong...call your congressman.