You may think the notion that radio should pay for playing music is crazy, but as mentioned above the US is perhaps the exception. It's been established practice in the UK for many years that radio pays for playing the music, regardless of the benefits the artist enjoys from having their product played to a large audience.
Clearly both sides benefit from the arrangement of music being played on radio [fills airtime with content that listeners want and musicians get their product publicised]- what is at issue is who should be paying who and in what proportion to the overall benefits received.