In medicine, you tend to need very specific treatments. This means the set of potential suppliers is much lower, which essentially means the supply is restricted. If you won't sell me an epi-pen for less than 100 dollars, there aren't a lot of places I can turn to. Moreover it's not like open-heart surgery is going to work.

Besides, some procedures are just actually expensive. Open-heart surgery takes a lot of labor, organ transplants require intense logistics. Dialysis is a complex and repetitive procedure. The 'fair price' for these in the economic sense is still high. Way to high for most people's morality.

Should people really have to chose between death and the bankruptcy of their entire family? Because in a functioning free market, it is near essential that some people have demand for something they can't pay for. So if we turn dialysis, heart surgery, etc. into free markets, there are going to be people who need those treatments that cannot pay for them.

Isn't that exactly what happens now?

Would you tell the people that needed epipens "well just have some paracetamol instead".

There are other examples, such as complex surgeries that would illustrate the point you're trying to make better.