Richard Bridge, if a surgeon saves my life with his scalpel, I "owe" my entire life to the surgeon. With every breath I take I "profit" from the surgeon's work. Yet I don't think you would interpret your principle to mean that the surgeon should be allowed to enslave me and all heirs I might have subsequent to the lifesaving surgery, on the theory that all my "profits" should be diverted to the surgeon. The whole point of living in a society is so that we can all profit somewhat from each other's labor, as well as each by his own.
So with the public performance right. Just because the tavernkeepers benefit from musical performance it doesn't <automatically follow that the rightsholders (who may or may not be the authors) must have a share. The law creates a public performance right as a gimmick, in order to make the copyright monopoly reasonably effective. But the law can define the boundaries of the gimmickry in many different ways. It's an arbitrary policy choice.
As it happens I think that the exemption for smaller taverns (if that is what the final version of the act contained) was not well thought out. What is truly needed is a revision of the applicable law governing ASCAP and BMI. That may be a long time in coming, though.