Again, you have got the wrong end of the stick.
PRS charge premises that hold live events, as far as I'm aware do not charge musicians. As far as the law is concerned, it is the person responsible for the premises who needs to pay for the public performance.
Also, Bert Jansch and others pass over their rights to PRS to collect royalties on their behalf, otherwise any time a premises played a song it would have to ask the individual composer each time. So royalty collection societies are not 'all-bearing super powers', but societies working on behalf of musicians.