There are too many wealthy people in the U.S. for private healthcare to be outlawed. Further, hopefully such a ban on private enterprise would not pass Constitutional muster at the Supreme Court.
In any case, there are too many rich leftists who still want their private doctors.
After 2010, private healthcare insurance was basically outllawed. You could only get it through your employer. If you were an entrepreneur or worked at a place that didn’t offer healthcare, you were forced to buy Obamacare, with a hefty ‘fine’ if you didn’t have any healthcare insurance. My brother, who lived right on the edge of financial failure, had to pay the fine a few times. Other years he was enough under the poverty line that he wasn’t fined. He was a Bernie supporter who wanted Government healthcare so he didn’t have to pay for it. He died relatively young as he never went to the doctor.