doctors and antitrust laws

Would it be fair to plumbers if everybody got together in a state and said to the plumbers this is a schedule of what we are paying for your services, for instance, unclogging a drain. Take it or leave it. The plumber could either accept the rate dictated by the population or be excluded from the base of customers. He could elect not to accept that schedule of fees but he would likely have no customers as the population would elect to go with the plumber who accepts the reduced "negotiated" fee.
It is likely in such a scenario that incomes of plumbers would decrease and thus people would be less likely to enter the profession of plumbing. This would result in smart people going into other professions that are not forced into fixed fees. The outcome is fewer and less desirable people entering the field and ultimately poor service to the population.
You may ask why don't the plumbers get together and say none of us will work for the reduced fee schedule. Therefore, forcing everybody to negotiate individually with the plumber. In fact, this violates anti-trust laws and is prohibited. The plumbers cannot get together and discuss and/or set their fees. The spirit of this law makes sense as it would be unfair for all the plumbers to decide on a fee together which limits competition and forces a specific fee for a service. By competing with each other, the plumber will try to get a price lower than his competitor to get the business.
It is unfair that the population can get together to negotiate fees but the plumber cannot. It seems to me that their should be an even playing floor. If the population can negotiate as one (collectively bargain) then the providers of the service can do this as well and bargain as a collective group. On the other hand, if the population cannot or does not have the structure to collectively bargain then the provider cannot as well.
So where am I going with this?
This is analagous to the situation currently in place for the doctors. The fees are set by the insurance companies. The doctor can take it or leave it. The insurance companies are effectively collectively bargaining for the population but the doctors are unable to assemble to bargain as one entity due to anti-trust violations. A single doctor cannot take on an insurance company to effectively negotiate fees.His only options are either to accept the fees and see patients or reject the fees and see minimal or no patients. This is price fixing and needs to be changed.
As usual it will be the public that loses. Ultimately, the fees forced upon doctors will be so ratcheted down that the doctor will be losing money resulting in him dropping the insurance companies (this is currently underway). This will lead to less access to doctors under people's insurance and the doctors that do accept the insurance will likely be of poorer quality. That is because the only way the bad doctors would be able to attract patients is to remain on the list with the insurance companies, otherwise nobody would go to them. Additionally,when a patient wants to see a doctor outside the insurance company, he will likely incur significant fees which he/she would be responsible for. Again, the public loses.
Another outcome is fewer young people will enter a field where the value of their services are determined by a beurocrat or politician.
The fair resolution to this problem is easy. If insurance companies collectively bargain for their population then the physicians can collectively bargain for their services. Seems only fair.