I think it's his standard anti-celebrity message, and acts as a reminder that human works are temporary. For all we know, the greatest artist on earth could have lived and died without leaving a trace of their work behind. So in that sense, it's completely arbitrary who becomes famous and these art collectors are arrogant for thinking they should be the sole proprietors of artistic worth.
He also literally stopped them in the act of placing a label on him as a person or artist, and this way he retains control without letting his piece become part of another person's ego, basically. Sure, they will probably keep it and brag that they have a banksy, but how can they really display it now? These people own art, and they have an ego about it for lack of a better word, but they're not artists. All they have to do is spend money but they take other people's ideas and use it as a way to pretend they're artists too. Banksy has prevented the buyer from being able to entertain any illusions about being on his level. Sorry for my shit wording as im very out of it but his work is rarely meant to he deciphered and is pretty straightforward so I wouldn't look past that personally.