The problem with having two levels of Govt looking after health care is that there are cracks a mile wide with nobody looking at them.       Eg:  extra fee billing is in Ontario as well (likely other Provinces too).    Examples are:  "Membership fees" for clinical practices which are charged directly to the patient.    These fees are "optional", but opting out would mean that you would have to come in person for test results, prescription refills, etc.     In this way, a clinic can maximize revenue per patient, and physicians can work fewer hours and make a very decent living.

Canada's current health system is unsustainable because there are few checks and balances and a bloated multi-level Govt  bureaucracy looking after it.     The solution: Federalize the current bureaucracy (yes, this takes Constitutional change) so that there is a single socialized system across the country (vs 13 slightly different ones) and give doctors the option of opting out completely.     Few would.