The thought process is that an unruly passenger on United, for example, should be banned from all airlines and air lines so they can’t go cause trouble elsewhere.
I think the airlines are asking the government to step in because they’re not sure they can legally work together to ban people from all air travel. I believe a government process is the correct answer here but only with due process and guard rails.
I won't be surprised if entire industries have Shinigami Eyes style blacklists of people considered too toxic to be allowed any kind of business involving whatever that industry provides within a decade or so.
I seem to recall that American, United, and Delta all use/implement Sabre in some form or another, and possibly shared a no-fly/ban list...but, my memory is a bit hazy on that.
This is sort of already done with consumer credit agencies
The airline just wants the gov't to do something for free so that they don't have to put any work or expend resources doing it!
probably also lets them dodge blame. "oh you're on the no-fly list, take it up with the feds."