Providers will leave or retire as the profit motive is decreased. When quotas are implemented they will just do the minimums. The best and brightest will work outside the system to increase the profit motive. Routine things will be covered for more people, by less people, doing less work. Resulting in worse care and long waits.
Industry to attract the best and brightest will actually have to pay MORE money to pay for private plans to get people in addition to paying more taxes for the public insurance. So the cost to the wealthy will be more for less.
I know this because I managed a Canadian company for 8 years and basic understanding of capital markets and economic theory.