Uninsured Americans are in fact universally included in death statistics and in cancer survival outcomes; we have top-tier cancer outcomes.
Europe has several universal coverage systems without single payer. The original sin of the US system isn't private insurance, it's employment-based coverage; that's the thing nobody else has.
Again, you cite zero sources. Survival rates for lung cancer in the USA, the most common cancer in the world, are much lower than Japan and South Korea. South Korea is single payer and Japan has strict government regulation of healthcare costs.
The second most common cancer is Breast Cancer. The USA is "top-tier" but so is pretty much every other Western Country. Australia, also famously single-payer is a mere 0.4% behind the USA.
This is the only source of modern survival statistics by country:
https://pmc.ncbi.nlm.nih.gov/articles/PMC5879496/
Compiled into an easier to read format:
https://worldpopulationreview.com/country-rankings/cancer-su...
Take note of two things: First, some states weren't even included in the study and second, there is no mention of insurance. The statistics are only tracking people who were diagnosed with cancer. It's reasonable to assume that some people who had cancer symptoms did not seek treatment because they didn't have insurance and died without being diagnosed.