Not really. Private health insurance would still exist alongside for the more wealthy (including nearly everyone on HN) that doesn’t want to wait a year for their public system MRI. Same thing that plays out in other countries. The U.S. already has a form of this in so-called concierge / premium providers too. Lots of profit to be made.
Having the machine capacity to get non-urgent MRIs in hours is part of why US healthcare is so expensive. Anyway, the average (again for non-urgent MRIs) where I live in canada is 9 weeks, which is i am sure skewed due to the rural population. In the city it’s like half that.
If private health insurance was allowed, UHC would be stillborn. It only works if providers don't have better options than medicare reimbursement rates.
This isn’t true of the Medicare for All Act, for what it’s worth. That would ban private insurance altogether. Personally I think that’s a bug, not a feature, but if you’re very concerned with fairness then you probably think the opposite.