@JMarkOckerbloom Right, so it clearly fails the test of "Cooperatives are democratic organisations controlled by their members".
https://ica.coop/en/cooperatives/cooperative-identity
The current OCLC presumably exists to serve the interests of its own staff, i.e. maximising their wages and money extraction from universities. This is often the end result of 501(c) controlled by a self-perpetuating board.
Would a worker-owned cooperative avoid such a mismatch? What if members were workers at "customer" libraries?