Nice example you gave, because this literally happened between 2002 and 2015: https://en.wikipedia.org/wiki/No_Fly_List The No Fly List eventually swelled to close to a million people. There was no one entity you could sue, because airlines had their own algorithms for matching, so even if you werent on the list, but the algo fuzzy-matched you, you were effectively on the list. Matching names is notoriously bad. There was an ACLU lawsuit, but it was a much bigger effort than anything being described on this thread.

In summary: lawsuits against Government systems are slow and not necessarily something to aspire to as a better system.