The US system has the same issue -- many people don't have a regular family doctor and rely on clinics. It's a more complicated problem than pay -- family medicine simply isn't an attractive speciality to many medical students. Money could move the needle a bit, but treating strep throat is never going to be a prestigious pursuit versus a lot of other specialties. And if it doesn't improve overall longterm outcomes, it's not worth spending the money to move that needle.

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...).