You forgot a few rather important points
There is a difference between a songwriter and a performer. With this system I see no way for a songwriter to get paid at all.
Recordings often cost a lot of money to create. Musicians often have to be hired, as does expensive studio time. This money has to be recouped somehow. To create software all you need is a computer. To create certain types of recordings takes a huge budget that needs to be recouped somehow.
And your example about radio stations is wrong for several reasons:
Britney Spears wouldn't get anything from ASCAP or BMI. Her writers would though.
An ASCAP or BMI licensed station can only play a certain amount of music by any artist in a given period.
Most stations, and most large venues (ie those where any significant money would go to the writer anyway) submit playlists to the PROs so the money actually goes to the correct people...

Yeah, I accept that this is not intended for commercial songwriters, but the problem still remains. People who are interested in being paid for their work deserve that payment. You haven't suggested a way in which those people could actually be paid, which still leaves us with precisely the system that is already in place - all this would mean is that the small town band playing original material would still be paying Britney Spears' writers through ASCAP/BMI/SESAC/PRS/whoever, but they would have made a legal declaration that they don't want the money anyway!