Yes. Universal health care would eliminate the need to worry about payment. Patient care would actually focus on patient care, rather than patient affordability. Patients would no longer be turned away for failure to pay, or lack of insurance. This would widen healthcare to the homeless, underserved, underpriveleged, and lower socioeconomic status patients. If implemented properly, it would also help healthcare workers, as it might increase payment.
No, universal health care would not set a good standard of care, because each person can only receive the bare minimum of care. There is no way to make sure that a shortage of health care services can be fairly distributed. If the entire population cannot receive something, there is no fair way to ration it. There will always be winners and losers.