>Countries that have to pay for healthcare have a strong incentive to keep its population healthy to reduce healthcare costs

It doesn't work that way in practice. It's a weird argument and nobody would ever buy it as there is no obvious cognitive (and politically valid) path from climate change policy to healthcare policy. This is true for America, and Canada and Australia and I suspect every other country.

Also, your underlying assumption, that the American government either has no incentive or is uncaring with respect to keeping the American public health, is just wrong and probably betrays your ideology. Both parties, Dems and GOP, care about people.

Medicare and Medicaid together are the federal government’s biggest expense. That’s not counting other federal health care spending, like VA or ACA related items, nor does it count state contributions to Medicaid. Or CHIP for that matter.

About 20% of Americans have Medicaid, and about 20% have Medicare. There is some, but not much, overlap, so the total percentage doesn’t hit 40%. Health care needs to be better in the US, but it’s misleading to suggest that huge amounts (trillions of dollars) of government money aren’t already being spent on it.

If you look at the numbers, the various levels of government in the US spend more on healthcare, as a percent of GDP, than most(all?) European countries. So if this was a thing that would push policy on climate change, it would be a bigger lever in the US than in Europe.

the government is the citizens. The government has no money of its own, and can't pay for healthcare without taking the money first from the citizens.