I think that’s a fair expectation of government. It may be that the market can deliver care at the lowest cost but what if the market delivers that lower cost by limiting supply? Say they don’t offer service in some areas or limit some procedures?
Then the next question is: historically, which systems of resource allocation have been able to successfully avoid supply shortages of the thing in question, markets or government allocation?
If the (regulated) market can bring down equilibrium prices to the minimum, then the government’s role could be to provide health stamps or cash to those in need, similar to food stamps (which can arguably be reformed).