Right now a doctor tends to be in the "network" of many insurances at the same time, not a single one. Presumably that would still be true under a co-op system. Obviously the size of a provider network would be one of the factors that would make one insurance more appealing than another, but overall id expect you to be just fine switching providers and keeping your doctor.
Also keep in mind with PPO type insurance you are never required to get a referral so can see any doctor at any time, with out of network being slightly more expensive.
That said no reason an insurance cant be open to any and all doctors at an appropriate price point.