I don't agree that these are good reasons to make healthcare not a market. It's true that customers don't necessarily have a lot of ability to choose providers or price shop under our current system, but that's certainly not an inherent trait of healthcare. It could be otherwise.
As for not understanding what they're being asked to buy, what I'll say about that argument is it proves too much. Why do the markets for computer repair, automobile repair, etc. not have the problems that you claim would be inherent to a free market in human body repair? Understanding of the subtleties in those areas is equally out of reach to understanding of healthcare.