It's pretty obvious that creating an explicit profit motive makes things worse. This isn't a hypothetical, people in US pay far more for healthcare per capita than people in countries where there is socialized healthcare.
Doctors' wages have been decreasing when inflation is factored in just like all other workers, despite the skyrocketing costs of health care. Guess who pockets the difference.
In most cases it's probably fair to say that hospital administrations do not give a single shit about passing on those profits to the doctors, nurses, and other support staff. They will give the barest of minimum to everyone below while writing fat bonus checks for themselves or giving out pointless board positions to family and friends.