Yes, I know that one can still purchase supplemental care in single-payer countries. However, there are plenty of people in the middle who are paying full price for health care in America who wouldn't purchase supplemental care in a single-payer system. That will lead to less funding for advances in health care that people are willing to pay for. That is a bad thing.

Medical costs are rising because people have more and more disposable income, and they're choosing to spend it on the things they value most, like health care and education. Instead of letting that price signal serve as motivation for more people to supply the goods and services that people value most, single-payer systems force prices down and result in less investment in the products that people want to purchase. Forcing people to buy a product from a single vendor hinders competition. Forcing prices down by hindering competition is bad for the future of any market. It's a bad idea.