I can see that private health insurance companies wouldn't want to take in bad risks. They don't in some US states, and are forced to by the federal government in others, I can also see that a profit driven GovCo would behave like a giant private insurer. But actual in-GovCo governments are incentivised to provide universally access to healthcare as they do to the law and education. I can vouch that where you have public healthcare, any hint that some group is excluded creates a stink. Health insurance provides better incentives than piecemeal provision, but public healthcare has better incentives than both.