Yukon first had medicare in 1968-1969. It was probably not single payer at the time.
Canada only went to single payer after LARGE numbers of doctors started opting out. So many did this that the government passed legislation making it a federal crime for a doctor to receive direct payments for medical services. This had the effect of enslaving doctors. Today there are probably more canadian trained doctors in the US than here in Canada.
And yet the per capita number of doctors in each country is about the same.