I cannot see how the Federal Government could outlaw a private primary care doctor contracting with patients directly.
Much like the VIP concierge plans that exist now.
Of course - the government will become the only licensing agency.
They can, and likely, will. This was one of the problems they had up in Canada, they outlawed private practice of medicine and imaging to force everyone into the government run system and avoid people doing end-runs around it. They do have private practice, but it is publicly funded. So, if you are a doctor, you are paid by government money. You don’t play by their rules, you don’t get paid.
I fully expect that will be the same here when this is completely implemented.
Of course, Canada had such intractable issues with availability of imaging (big surprise there) that they have begun to allow private imaging centers to begin opening again to alleviate the backlog.
Nothing like allowing money to incentivize behavior. Funny how that works...Thomas Sowell, in his great books, goes on at length on why it works so well, and why free-market capitalism will kick the crap out of centrally controlled government every single time.