Also worth adding is that most of those uninsured are present in the country illegally. For comparison, UK’s NHS does not offer free services beyond primary care to those unlawfully present either, and I think this is true of most other public healthcare systems around the world.

But it is ethical to keep the lines shorter by excluding the poor?

No but that wasn't the question the OP asked. Unless you've got a nation of saints the majority of people will make somewhat selfish decisions.

And for most citizens of developed countries that selfishness translates to universal health care. No need to worry.