Two-tier systems work well in a lot of places, for instance in France.

Doctors everywhere else are public servants. They do their jobs because the love it, because it's their calling and because they still get paid very, very well. Canada pays their doctors $232,000 to $676,000 gross (speciality averages, low to high).

Then because malpractice insurance is also socialized (Canadian Medical Protective Association), their costs are significantly lower too. OB/GYNs usually pay the most, and in Manhattan their annual malpractice insurance premium is $125,000. $176,000 in Long Island. [1] The highest in Canada is Ontario, at $44,000 CAD ($34,000 USD).

[1] https://www.excellusbcbs.com/wps/wcm/connect/b7cdbf66-dd6b-4...

[2] http://www.amednews.com/article/20100503/profession/30503993...

The public hospitals in Australia are often really good and prestigious institutions used for teaching as well. So, while you don't get a private room and luxurious amenities you do see top doctors. I can't comment as to why they stick around the public hospitals. I don't know that they make less money doing that.

Procedures under the public system are scheduled by urgency, so for example you might have a 9 month wait for a torn ACL surgery. That's why most will carry private insurance. Private cover starts around $70 a month so it's much more affordable than US insurance and importantly much simpler to navigate.