How to regulate insurers

How about one price medical care? I am lucky enough to have medical insurance. I am always shocked when I see how much the medical provider reduces their charges when they are paid by my insurance. The uninsured have no such protection. Not only do the uninsured have to pay their own way but they have to pay a price that far exceeds what the medical provider evidently believes is market value. I wonder sometimes if the extra high billed costs are to force people into insurance. If there were a one price rule for medical providers based on an average of what they bill insurance and medicare for services, perhaps the uninsured could pay their own way and get medical care they need.