I think the US has better cancer survival rates in areas than other nations, but if that is all-around significant one would think that would reflect out in better life expectancy overall. However, the US is a huge negative outlier in life expectancy and child mortality with universal healthcare nations outperforming on those measures too.
The most recent life expectancy numbers are the hardest to interpret, the US has the only three-year-running negative life expectancy growth in the first world nations - but some argue we should separate healthcare from the suicide numbers that are a big contributors. I don't know that I agree with that as there is a fuzzy line between healthcare and social care efforts.
Life expectancy is a weird stat by which to measure healthcare outcomes. For starters, it responds rather strongly to demographics. E.g. having more males reduces life expectancy holding all else equal. There are many things like this.
Age-adjusted all-cause death rate is the better stat for measuring life-saving outcomes.
Child mortality is certainly a useful stat for its purpose, though.
WHO is the best source I know of for most things like this. I was unable to find the exact stat I was looking for, but here is e.g. data on all-cause mortality rate between ages 18 and 60:
