The value lies in the exposure: You don't make money from a video, but because of it. If you have a hit video, chances are you can make plenty of money elsewhere—by winning a traditional-label contract, touring, making ringtones, selling merchandise, gaining endorsement deals, and so on. If Black is going to become a tween millionaire, the money will come from somewhere like T.G.I. Friday's, rather than "Friday," directly.
And Ark did make that happen for Black. So while there may be no valid defense of her song, there is certainly a defense of the lighter, leaner business model that produced it. Ark might make awful music. But it does give its artists a shot at the limelight for a reasonable fee. Reportedly, Black's parents paid just $2,000 for the whole shebang.