The no-fly list isn't really a background check. It's just a simple name match, and it catches people who aren't on it because of that. An interview (like nexus

The no-fly list isn't really a background check. It's just a simple name match, and it catches people who aren't on it because of that. An interview (like nexus or customs) also isn't a background check. These are three separate things. Everyone gets a check on the no-fly list, some people get advance background checks (Pre and programs like it I'd expect), and fewer still get an actual interview (international travellers who also have to supply a passport). Having a unique ID number tied to other information about you (like your license ID number or passport number or SSN) allows for a more in depth check, no doubt in ways you probably don't even explicitly consent to. If they did have your ssn or passport number from the airline at ticket purchase time then sure, that would allow for the same thing. But they don't. And if they did it'd be pretty expensive to do it for everyone. So, the current solution is basically just to make (some) people pay for their own background check.