A broken clock is right twice a day, but still broken.

Why

Perhaps it's worth pointing out that progressive liberalism and worker cooperatives are not as aligned as you might believe, but that's probably too off topic. Worth doing some reading about though.

Co ops can have traditional chains of command, the only defining characteristic of a co op is ownership. There's no reason why a leadership hierarchy and leader ownership must go hand in hand.

A well-functioning co op can take in any worker irrespective of work ethic and provide them with the structure and support to develop into a valuable team member. The problem is that co ops, like anything aren't guaranteed to function well.

So no, a co op does not require all workers within in be fundamentally minded towards the business. A co op simply means that the ownership of the company and the labour force are one in the same. There are plenty of co op workers all over the world who just show up and do their job, they just also have a voice and must be considered differently as a result.