In Canada the typical MRI waitlist time is several months outside of emergent issues. You could go privately but it's tougher than you think to pay for this, as it's not well integrated with the public system and your family GP (if you have one). I guess I'm saying, cost is definitely one factor but our exclusive public-only system has got problems too
Canada has extremely few physicians, like USA. For healthcare to work well you probably need to reform your system to get more physicians, I don't think any system works well when you have too few physicians. You can see the countries with good public healthcare has twice as many doctors as Canada and USA does.
