Define profit.
Profit, in economics, means above and beyond all costs. Including salary. Including benefits. Including the money required to reinvest in your business to keep it going. People say profit when it isn't what they mean at all.
Many hospitals and insurance companies are not-for-profit. There is a fine line between non-profit and NFP; it is a legal distinction. A non-profit is just that; it cannot make a profit. A NFP is a company who can make a profit, so long as the profit is reinvested solely in enlarging the company, not in making new acquisitions of smaller companies or the like.
If I were in charge of reforming health care in this country, this is what I would do, for starters. Create a government run health insurance company that charges premiums on a sliding scale. It would be setup in a such a way that, while not entirely self-sustaining, the cost to the tax payer would be minimized. Policy decisions would be made, not by politicians or businessmen, but by qualified medical professionals on a board of directors which would be comprised of members nominated and confirmed by the medical community in some capacity. There would be term limits, etc. Jobs would be given at the admin level to people with insurance industry experience.
It's really the only way I can see that would clean up the mess we're in. We don't want to go frying pan-fire with an entirely government run system; that wouldn't be much better than what we have now. However, the industry is so collusive, there is no 'free market', no real competition, and without it costs skyrocket every year on both ends (insurance and medical care) without any checks or balances. It is therefore, in my opinion, the necessary duty of the government to either legislate them into competition, or provide a competing alternative. I personally favor the latter, because I think it would be more effective.