disclaimer: I am by no means and expert on the subject.

What I do know is that public places (bars, restaurants, shopping malls, etc.) are expected to pay royalties for commercial music that is played for public ears. The way I understand it is that these fees will cover commercial music being played live by a musician/band and also pre-recorded. I also understand that if a venue does not pay royalty fees, then it is the responsibility of the musician/band to pay those fees when playing commercial music. So it is not necessarily the club owners responsibility. The owner could choose to either not have music, or hire musicians who only play original material, or hire a musician who plays commercial material and pays the proper royalties. Based on your last paragraph where you said "if you (venue) profit from the intellectual property rights of others (songwriters), you must buy a license so that royalties can be paid to those who created the intellectual property I would think you agree that if playing somewhere that does not pay royalties, then it is up to the musician to do so, right?