(1) It’s expensive (2) Everybody has to pay (3) The government’s gotta run it
But there are plenty of countries with functioning healthcare systems that are private? The Swiss, for instance. Moreover depending on what counts as "government’s gotta run it" (paying for it? administering it? actually providing care?) you can argue that the German or even Canadian systems aren't government run, at least to some degree.
"There are people not good enough for health care and helping them would violate this natural order".
That doesn’t make it the wrong policy decision. Lots of systems we happily manage with similar dynamics. But I don’t think denying that basic fact is the right path forward. The moral hazard is real and worth acknowledging.
Smokers for example have more lung disease and cancer which cost money to treat, but usually not until they are in their 60s so they still spend their entire life paying into the system, but then they die soon after, saving on age related healthcare costs. And that is on top of smoking disqualifying someone from many treatments and surgeries, making smokers a net-win for healthcare costs to society.
Being really fat also seems to have similar effects, although the the finances are much closer so perhaps the second order effects from being fat cancel them out. But on paper they are still a bit cheaper than the average person.
Many people will argue against it because it "feels wrong" and they think unhealthy people should be punished (for example with higher insurance fees) and don't want to admit that unhealthy people are subsidizing their own healthcare, doubly so if you add in the sin taxes they have been paying their whole life that often result in more state income than their entire life-time medical costs add up to. But there has been numerous studies across the decades in Europe and the US showing how much cheaper unhealthy people that die earlier are to care for compared to the 90 year old granny walking everyday and risking broken hips and taking 30 different medications a day.