For government sponsored health care to function properly it has to regulate what medial procedures and drugs cost.
That's correct. Now if the prices were set with the goal of having the patient pay, then the market itself would regulate this. There would be not need for government to do this.
Btw, you even see a similar logic when you have an accident and go to the body shop. As soon as the shop realizes your insurance will pay, they inflate the amount of parts and costs needed to repair, as opposed to being a lot more judicious if they realize the cost will be paid by you.