I have direct and relevant experience with both the US system and a single-payer system (Japan*). I struggle to think of any areas in which the US system is clearly superior. Waiting times for appointments are shorter, quality of care is absolutely first rate, and the costs, including insurance premiums and patient out-of-pocket, are far lower. In the US, the quality of care is excellent (if you can get it), but the financing system behind it is broken on a massive scale no other modern country on earth even approaches.

* Japan's system isn't a traditional single-payer system in the European sense. Rather it's a universal statutory health insurance system (SHIS). But for this comparison, that's splitting hairs...