The free market is very good at reducing prices in some areas but then it would also not serve other areas where there is no profit. So in a free market health system you would see cheap prices for some stuff but people with certain diseases would just be left to die. You would also see a lot of bad drugs that kill people.
Also, the free market can't co-exist with heavy regulations - you can't just make insulin product and start selling it - you have to go through FDA first, and then market it to doctors who is an ultimate gatekeeper for the drug.
