Ugh.
Government distorting undeveloped markets that have a lot of room for competition to increase efficiencies is a bad thing.
Government agencies running programs that should not be profitable, or where the only profit to be left comes at the expense of society as a whole, is a good thing.
Lots of basic medicine is the go to example here, treating cancer isn't going to be "profitable" and attempting to make it such just leads to dead people.
On the flip side, one can argue that dentistry has seen amazing strides in affordability and technological progress through the free market. From dental xrays to improvements in dental procedures to make them less painful for the patients.
Eye surgery is another area where competition has lead to good consumer outcomes.
But life of death situations where people can't spend time researching? The only profit there comes through exploiting people.