The club would have to be a huge, multi-billion dollar organization with a strong central leadership and lawyers to enforce the rules for distribution of the music. In other words, a...... ;)
The rhetorics about "bad" major labels (or "mega-cooperations" as Stallman likes to call software companies) is just that: rhetorics.
However, there would still be an important difference: Club members are less likely to upload stuff to others, since they would harm themselves, only.
On a side note: I don't think it would need to be huge. There are quite a few small independent record labels out there, concentrating on one kind of music. So could any club.