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.