Well for one, it would be illegal. Governments at the federal and provincial levels have passed legislation forbidding it with penalties as high as $50000 for violations (in Ontareowe) .  It would be financial suicide for those docs willing to go this route. 

They have also weakened the public system at the same time.

We have the worst of both worlds.

A weak mediocre public health system and no private system to drive efficiency or pick up the slack.

Every other country except North Korea allows private competition for physician and hospital services. Almost all of them perform better.  We used to outperform the US.  Not any more.