Bad analogy. You buy a book, you dont buy the right to copy and distribute it. I buy a CD, or turn on the radio which I have bought, I am entitled to play it. As long as I am not (directly) charging people for the performance, then there is no problem. Any profit the establishment makes from the music being played should be offset by the exposure the music gets to potential purhcasers. This isn't the same as making copies of a product and handing it out for free.
That's not what the copyright law says. The recordings are sold for private use only, no public performance, same as videotapes.
How about if I rented a DVD and showed the movie at my coffee house or bar? "Come see free movies every night!" I could say. And I'd make more money, because people who wouldn't come to buy my coffee WILL come to see a movie and THEN buy my coffee.
It doesn't matter whether you're directly charging for the product or not. You're enhancing your profits by using someone else's work. If you don't like their work, or think it's too much, do the capitalist thing and turn it off.
You're wrong. Read the copyright law. Public performance is a specific right of the statute, a right possessed by the copyright owner, not you.