Actually I think you have more leverage than the Dr. If you are not happy with the insurance company you cancel the policy or complain to your employer (you are paying them, the insurance company does not want to loose the business). The doctor can do nothing - they want to get paid, they have nothing to hold against the insurance company.
On the other hand, a little bit of work done by a lot of people vs. a lot of work being done by one office, the "crowdsourcing" sounds like a better solution. The obvious down side is that I have no leverage against the insurance company - a doctor's office does.