clubs that are licensed for live music pay some kind of fees, if I understand the situation correctly -
They're supposed to. BMI and ASCAP require yearly licence fees for playing the music of artists and composers that they represent.
And they have a pretty extensive enforcement network, too, stopping in bars, clubs and restaurants, looking for not only live acts, but places where a radio station is being played for entertainment. I've heard stories of owners of the tiniest open mic venues in the smallest of towns receiving 'cease and desist or pay up' notices.