As far as i know current insurance isnt prone to corruption as the major issue driving price, it is prone to greed, which is a legal though undesired factor that is very different from corruption.
As for the smaller co-ops not having negotiating power, since no insurance is driven by greed who would they competing against to negotiate. There would be no motivator for insurance to have **exclusive** deals. Doctors would want the largest networks, and insurance companies would want the largest, and there would be very little preventing that in most cases. Expensive doctors might prefer more expensive insurance, but if the patients of those doctors are likewise the owner inthe practice (not just in the insurance) even that goes away since the doctor is no longer setting their own price, their owner (the patients) are.