Single payer in the UK has already led to doctor shortages, so I'm not sure what point you're trying to make.
There's many ways to get to a shortage, cartels and single payer are but two.
There's many ways to get to a shortage, cartels and single payer are but two.
Source? The only news i've read of shortages are Brexit related.
Fun fact: the doctors were the biggest obstacle to the foundation of the NHS and they disappear into private practice at the first opportunity.