Another potential alternative is healthy capitalism, where a large number healthcare providers are in competition with each other to provide the best service at the lowest cost. In this model a hospital, for example, would be forbidden to buy another hospital down the road, in the same way a doctor’s office would be forbidden to buy a second doctor’s office, because both cases reduce competition.

That would be government. Markets don't regulate themselves and monopoly is the natural equilibrium state of capitalism.

No, it would be a mixed economy, where private individuals and businesses provide most of the goods and services, and the government plays a significant role in regulating the market.

Monopolized markets are almost always evidence of regulatory failure.

"Healthy capitalism" isn’t an option distinct from government intervention. Healthy capitalism it is government-regulated capitalism. Any system where competition is protected depends on active, ongoing government enforcement of the rules. Without that, markets naturally tend toward monopoly or oligopoly.

Advocating for "healthy capitalism," is advocating for a system where government sets boundaries and steps in to preserve competition. That places it firmly within the spectrum of government-regulated options, not outside or apart from them.

It's tempting to imagine ideal or the worst versions of each option and then claim, "what I want is none of these." Instead, we should look at whether our preferred scenario is actually possible within the real-world range of choices. In this case, "healthy capitalism" is only possible when government is both the referee and the enforcer, so it's a version of the government option, not a separate path.