I agree with you free market is better than government subsidies, in general.
The only problem is: when I can't afford healthcare, I will not care if it's the government or the free market. I'm just sick and cannot afford my treatment.

So we can't just stop free healthcare / subsidies and say: everything would be all right if we were in a free market system with high level of competition, because we're not in that system...

Before Obamacare (not that I like it) US had one of the less "public" healthcare in the world, but poor people were in big trouble.