Why should the Board give them rates lower than what they can get by freely negotiating with the copyright holders? The answer is in your own post:

Why should the Board give them rates lower than what they can get by freely negotiating with the copyright holders? The answer is in your own post: The purpose of the compulsory licensing scheme is the public good, to keep copyright holders from preventing certain socially-beneficial uses. If traditional radio compensates rights-holders as a form of advertising, why doesn't internet radio (which has restrictions on how often and how predictably it can play music)?