I'm Canadian and can't get a family doctor (nor can my wife). I don't consider that a "good deal". Maybe if it was more lucrative (read: doctors made more money, budgets were higher) we could attract more talent and I could?
At any rate, it's rarely impossible to find a family doctor, but it can take some persistence to find one accepting new patients. Almost every provincial medical association maintains a list of family doctors accepting new patients. If you're in a small town it might be a challenge, though.
edit: to put some numbers on this, 15% of Canadians don't have a family doctor (http://www.ctvnews.ca/health/canada-ranked-last-among-oecd-c...). In the much higher spending US system, 20% of Americans don't have a family doctor (http://www.fiercehealthcare.com/healthcare/one-five-american...).
Worth considering:
Per http://www.chcf.org/publications/2016/05/health-care-costs-1...
> US health spending reached $3.0 trillion in 2014, or $9,523 per capita, and accounted for 17.5% of gross domestic product (GDP).
The Population of Alberta is around 4,196,457 per a statscan estimate for 2015.
4,196,457 * 9,523 = 39962860011
So we're spending ~20,000,000,000 CAD = ~15.5 Billion USD, versus 39,962,860,011 USD for the same population in the US.
edit: The US number seems to include prescription drug spending. Per http://www.statista.com/statistics/436305/medication-spendin..., it's $867 per person in Alberta, or $3,638,328,219 CAD -- so it's closer to $18.5 Billion USD for health spending in Alberta.
That's a better deal any way you look at it, especially when you bear in mind that Canada has better overall outcomes than the US.