The R&D, which costs millions (and sometimes billions) still needs to be paid for by someone..and the government just isn't efficient enough to do this effectively and within a decent time frame.
The problem isn't for-profit healthcare. The problem is the insurance companies. They create an un-needed middleman that inflates the cost of everything. A better alternative would be to get rid of insurance for most things, allow doctors and hospitals to charge directly to consumers (which would bring the costs way down).
Surgeries would also come down in cost because of competition. The ones that don't come down are most likely because they are rare and have little competition. These can be covered under insurance.