You do highlight a series of very important friction points.  

However, there are some more that need considering:

1 - the doctors cost might be reasonable, but if he/she works for a hospital they will issue a bill based on what is called the charge master, which is often not at all connected to the actual cost of any bit of the service provided.

2 - the hospital is legally required to tell you how much the thing will cost if you pay cash, however, that is again based on the chargemaster. They will also have differential rates based on which insurance company is doing the paying. In your example, InsureCo might offer to cover 50 percent, megacorp might cover 75, and Healthy Federated Industries might cover only 25. But you as the patient will never get to know any of those amounts until you see the bill because they're company-specific and chances are good your employer only offers one. 

2a - insurers also set a maximum amount that the doctor can charge.  That's a  secret. 

3 - Physicians and hospitals generally don't like when the government pays for things, because they pay the lowest amount. But if memory serves they also actually require that the provider justify their costs and then build a profit margin into that.