In practice that's not really how it works any more. Most "insurance" companies don't provide much actual insurance. Instead they act as third-party administrators for self-insured employers and other group buyers. Those customers are very price sensitive, so insurers have a lot of incentive to drive down provider prices in order to maintain market share.

What's increasingly breaking the free market is provider consolidation. In many areas most of the small medical practices have been bought up by larger organizations. So those large providers control so much of the market that insurers have to pay whatever they charge. For example, in Northern California if an insurer (other than Kaiser Permanente) doesn't have Sutter Health in their network then their plans aren't viable.