I don't hear a lot of complaints about medicare not covering important things (but I only have limited exposure to that), and I assume a US single payer system would essentially be Medicare for all. I do hear complaints about Medicare not paying providers enough, and a lack of available providers.
A rational method of rationing care seems preferable to the current byzantine methods. My (likely naive) hope would be that spending the same amount of money on healthcare, but with fewer parties involved would provide more and better healthcare. At least we haven't reached the point where the government encourages smoking to decrease long term healthcare costs.