No single payer system spend all the money they could on their healthcare system. I think this is what most people are missing. You could tax people 100% and you still wouldn't have enough to make your system as good as it can be.
Plenty of single payer systems decides how long they are going to keep someone on treatment, what kind of products they allow them to be treated with etc.
A single payer system is based on a budget which means that budgets size is based on how it's prioritized.
It's easy to sketch convincing strawmen. But if you could actually point to somewhere that is choosing between kidney transplants and bullets, I'd eat my hat.