When you define the problem as you do, no wonder you think as you do. No one is taking away constitutional rights (nice tie-in) from health care providers. If they want to stay private, then let them. Others can decided to work for the public good at govt. lower rates. 
No one is claiming they are "servants". Again, a straw man fallacy.  These providers willingly chose their profession, that makes them different from bankers. And you use teachers who do work for the govt? 
(actually,  high costs are taking potential care and sending it to other countries, denying doctors of business.)

"Try to negotiate a discount?" From what, $50,000 to $25,000? Pay $25,000 by installments when you get sick at 60 and your income is barely above the poverty level?  And we think private charity has the money? I've read all those "answers" on Breitbart. They are all options now.  And is that working?
Let's close the socialized emergency rooms and let people die. It's simple free market capitalism.