Why doesn't america want a tax payed healthcare system (nhs) for poor people only?

I can understand why america doesn't want a full nhs like the uk but isn't it selfish that a poor family still has to pay if they are sick and then be in dept? What I'm suggesting is if you earn under a certain amount then you pay taxes and get free healthcare (like obamacare but totally free because... show more I can understand why america doesn't want a full nhs like the uk but isn't it selfish that a poor family still has to pay if they are sick and then be in dept? What I'm suggesting is if you earn under a certain amount then you pay taxes and get free healthcare (like obamacare but totally free because you pay with tax) but if your earning too much money then you have to pay and you don't have to pay healthcare taxes because your paying full price for your healthcare.

Rich people would probably prefer to pay full price anyway. But why make a poor family or a very sick child suffer because the rich don't want to help the poor even when it wouldn't affect them?
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