That's assuming the prices they agree on are optimal, which implies they have all the right incentives.
They could be paying too much in some cases (and then healthcare costs more than it should and some people can't afford it and die), or not enough in others (and then we get less medical R&D and more people die).
It's not an easy problem. And we can't just hand wave it to "have the government do it" as if they have some magic price-finding method that isn't susceptible to principal-agent problems or bureaucratic inefficiency or regulatory capture.
