It will?
Well, so much for Medicare. So much for Department of Veterans' Affairs hospitals, not to mention the military medical system. So much for the United States Public Health Service, the collection of any vital statistics concerning the incidence of different illnesses and mortality.
Since you speak of government generically and do not specify the federal government, so much for your cops and firefighters being trained as EMTs. Helicopters being very expensive machines, even before you put an RN, EMT and a commercial instrument or airline transport qualified pilot aboard, so much for any system of aerial emergency transport.
No more disability payments at any level of government. After all, by definition they are paid for reasons of physical or mental health. No more government sponsored student loans or grants to medical, nursing or hospital administration students. nor to students of any related profession. Nor to the schools.
The moment the framers of the Constitution put "promote the general welfare" in the preamble, they opened the door to government involvement in health care. All we're discussing now is what it should and should not do after it's walked on through.