How is that different than a single payer system? Those who earn more pay, those who earn less and pay not taxes (or worse, get free gov cash in the form of credits) pay nothing. Either way those who actually pay will pay for those who don't.
And yet it still doesn't address the problem of cost. No politician has a clue why health care costs so much. It's not because of insurance. Insurance is a middle man, and yes they take their cut, but it does not double the cost of health care. Government is a middle man and would take their cut from a single payer system also, and we know how inefficient the federal government is, so there's likely very little savings there.