This is very far from the truth. Worry not, rich people can spend to their hearts content in single payer countries. They still spend less and have better outcomes.
In the abstract maybe we do want to spend a lot of money for health care. However, medical costs have been growing at double digit rates. Hopefully that pattern does not continue for too much longer.
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.
The median real income has been hardly been growing at a fast rate. You'd need it to get growing at an incredible 10% a year for your explanation to be at all credible.
I didn't say incomes were rising. I said disposable incomes are rising. I can't find data to back that up, especially since the economic definition is different from the colloquial meaning of "disposable income." However, it's clear that technology has made both the necessities and luxuries of life far cheaper over time, which leaves more money for us to spend on other things even with a stagnant income.