The further you get from a perfect market, the less free market dynamics work. And even if they did, there's nothing in the theory that would minimize for patient deaths. The theory says that as patients die, people who are living would go to hospitals with better outcomes. But to achieve this outcome

1. patients need to be able to actually choose where to go. If they are incapacitated they have no choice in where they are taken.

2. we have to endure an unknown number of deaths for an undetermined period of time while we wait for the market to reach equilibrium.

So it's pretty clear free market dynamics are not the way to go when it comes to the healthcare marketplace.