I live in Mexico and pay for private health insurance because I want nothing to do with the government ran health system. Don't know what makes you think it's one of the best ran in the world.
I have also lived in Mexico (as an expat) and was blown away by the free public healthcare system. After seeing the doctor, I asked how much the diagnosis and treatment would be. The nurses laughed at me, said "Aye guerito, que lindo", handed me a prescription and sent me on my way.
If the same issue were to come up here in the US, I would have 2 options:
1 - with current ACA insurance - pay $200 + 50% of cost = $700
2 - with no insurance - about $1200 out of pocket
Which option do you think I (and most other people) would prefer?
I pay for private health care also because Dr. SIMM either isn't available or isn't convenient for me. But the fact remains that health care that works for the vast majority of things modern medical science can actually improve is available to every citizen.
And the thing that makes the system one of the best in the world is that it provides care at prices that middle class people can afford and where those prices are public quickly and easily to everyone. And it does so with a relatively small cost compared to GDP.
Compare that to the expense of Canada's system or the insanity of the USA system.
If the same issue were to come up here in the US, I would have 2 options:
1 - with current ACA insurance - pay $200 + 50% of cost = $700
2 - with no insurance - about $1200 out of pocket
Which option do you think I (and most other people) would prefer?