The cost of insurance is outrageous because settlements in medical malpractice lawsuits are outrageous. Tort reform is necessary to control medical costs - it is opposed by Democrats in the US. Trial lawyers are an important and generous lobby.
There are patients that make a living going around doctor offices and suing them. I know 1 patient in particular that went around suing doctor offices because they would not cater to his blindness. He would threaten a lawsuit without setting a foot in the doctor's office.
He would browse the doctor's website and complain it was not blind-compliant. And start from there.
Why assume the problem is the legal system and not the doctors? Maybe their performance is the problem.
For example, last I saw, hospital error was a leading cause of death in the US. Until recently it was hard to get doctors to wash their hands between patients, or follow checklists to ensure quality. There are stories of an omerta-like rule of silence about surgical errors.