Thats a common argument, but relying on the profit motive to fund healthcare leads to a clear priority mismatch. Years of expensive treatment is more profitable than a single dose cure. Vanity problems of the rich (hair loss, wrinkles, skin sagging) have a higher priority than problems of the poor (AIDS).
I have no reference atm, but I'm sure I read that medical research gets most of its funding from public bodies anyway. Its a lot anyway and I'm not convinvced that it wouldn't be better to be done all publically.
Who will fund expensive medical research for new drugs if the company next door can just clone your work with minimal expenses?
You have to address the free rider problem here.