Healthcare as a government service is one approach to the actual goal, which is healthcare that maximizes the quality of life and productivity of the citizens, rather than maximizing the profits of the providers.
When goods are discretionary and there are no externalities, it’s fine to have a purely autonomous market solution. Healthcare fits neither of those criteria. There’s a reason we don’t (or at least shouldn’t) have private subscription markets for baseline levels of law enforcement, fire prevention, public transit, food and drug quality enforcement, etc. etc. That same reasoning applies to healthcare.
Capitated reimbursement is a hybrid approach that helps a bit, but you can see from Medicare Advantage how the private sector relentlessly games the system because that’s how the incentive is inherently set up by the for-profit nature of the providers.
Yeah capitated reimbursement moves the risk but doesn't seem to effectively encourage innovation on care delivery when it's relatively easy to just cut costs at patients' expense because they have no agency and meaningful recourse.
Your criteria for when a market is (not) a good solution seem reasonable. My biggest concern is there's a fundamental problem with scaling labor-driven services that's exacerbated by entrenched interests constraining the labor supply to support wage growth. Care delivery needs to change if you want to fix both cost and quality, and I have a hard time imagining monumental changes to care delivery from a government service. Care will be expensive as long as it's constrained by scarce labor. That means either costs will balloon at the taxpayers' expense, service quality will decline to cut costs, or more likely both.
The way you fix that is either a) dramatically increasing the supply of qualified clinicians, or b) automation. Clinicians don't want more clinicians because it lowers their wages, so it will be fought at every level in the name of patient safety. But they also don't want automation to decouple care from their labor, so automation, too, will be fought at every level in the name of patient safety.
Most of this is opaque to voters who are largely under the impression that it's all health insurance executive greed, so there's not much of a political incentive to impose meaningful changes.
Where's the way out?