We don't have a free market in health care at all. In a free market you would be able to buy a coronavirus vaccine right now, instead of waiting months to get it for free. We haven't had a "free market" in health care in my lifetime.
Are you suggesting that it's better to distribute the vaccine in a way that keeps those most likely to get it vulnerable for longer (i.e. inefficiently)? What's exactly is the benefit of a free market in a situation where it's less efficient at allocating resources than central planning?