Interesting thought.
I foresee a problem, though. If you must join a co-op to receive care, and can only join one co-op at a time, then the vast majority of care providers are unavailable to you because they belong to a different co-op.
Moreover, you can't leave your co-op for another one without leaving your entire care team behind and assembling a new one from scratch. You're locked in.
It's like US health care's “out of network” problem, except even worse.