The upside to no parity is it creates enduring stars of the league. Even if you don't know basketball you can see Lebron is everything when he's on the floor. That, combined with the distinctive height and builds and visible faces and bodies of an NBA player (helmets/pads in Hockey/NFL, caps+short people in MLB), makes the kind of internationally recognized superstars that the other 3 struggle to create.
That and a few other things:
It's a sport anyone can play, you just need a hoop. The other big 3 require more set-up/equipment/people to field a decent game. This makes it easier to relate to the game, that I can just go to the park at any time and play myself. Basketball doesn't win in competitive parity, but it sure beats the other 3 at 'can I play it myself' parity..
In the bigger picture, maybe this is a controversial opinion, but I think a league populated mostly by visible minorities and internationals made it a 'cool' sport for non-US countries and minorities to follow. Maybe it's just my own experience but as a visible minority myself I was drawn to the sport that I saw all the other visible minorities playing as a kid.