I don’t think that “for profit” is the big issue, as the insurance companies are only making a profit of about 1% of turnover. I expect the issue is a lot more due to duplication of services, and unneeded tests etc done due to the risk of being sued. Also, the "best" drugs being used, without any proof that the improvement in outcomes, is worth the costs. And a system that stops cheap drugs being approved, and allows doctors to take payments from drug companies.
Until the legal system in the USA changes so doctors can take the risk of not doing anything unless it is clear that action is of benefit, rather than the current system that requires the doctors to prove they have taken all actions possible, not much will change. For example, disabled children are a fact of life, not a reason to cut most mothers open to protect the "no claims" discount on the doctor's insurance.
Doctors are also paid a lot more in the USA then the UK, in France they are paid even less, but seem to have a happy life unlike doctors in the UK.