Many nations have better health care than ours -- systems that actually improve people's health rather than threatening them with financial ruin for mediocre and inappropriate medical care.
The U.S.A. doesn't have to invent anything new, we can simply choose the sort of universal health care system that we think will work best for us. Our nation isn't so "exceptional" that we have to build a universal health care system entirely from the ground up.
If I could change our health care system I'd make medical school, nursing school, and training for other medical professions free. Graduates of these programs would work a certain number of years (not many...) in public hospitals and clinics located in areas that currently have no easily accessible health care services. These medical professionals would be paid enough, and the working conditions would be pleasant enough, that most stayed on when their contracted service ended. This would be paid for by progressive income taxes on the affluent and wealthy.
The current system of student loan repayments for similar work is broken and not beneficial to anyone but those who game our monetary system.