In countries with public healthcare it’s still based on ability to pay. You pay out of pocket and cut the queue, have decent time allotment with the doctor, get best medication available without money-saving algorithms etc.
In Canada private health clinics can not legally provide care that is covered by the Canada Health Act.
EDIT: After further reading it appears that private health care is a murky area in some provinces. My above stated belief appears to be wrong at least in terms of how things actually work there. Here is my view. Private medical care should be banned.
Here in backwater Europe we had no private medicine for a long time. The outcome was massive healthcare black market. Semi-official price list you've to pay to nurses/doctors/etc to „premium“ care.
On top of that, official medical staff wages were crap. People were forced either work for peanuts (IMO nurses and doctors jobs are damn hard and they have to be paid well), take money under table or... emigrate.
Now we have mixed system and it's definitely better than it was before. Doctors gets paid well. Elite doctors tend to work 2-3 days in private clinics and then 2-3 days in public hospitals so you can still get hold of them for free. Those who have an inch for premium services can pay local&legal, so local economy wins.
Do they? I was under impression that all US politicians aside from Sanders support current system.
Anyway… I think both systems are very similar in the end. Rich (or even middle class) gets great service in premium facilities. Average folks get OK service with some downsides, likely paying out of pocket in various ways. The only difference may be poor people coverage which is subsidized by upper tier payers. Who themselves may never use public service and go to premium only.
Also, another major difference may be the big expensive procedures. Aside from the 1%, people would do the procedure in public hospital because it’s crazy expensive otherwise. But everything else leading up to it and recovery after it more likely to happen in premium market since it’s much more affordable.
EDIT: After further reading it appears that private health care is a murky area in some provinces. My above stated belief appears to be wrong at least in terms of how things actually work there. Here is my view. Private medical care should be banned.