Because the data I've seen [1] doesn't suggest that.
[1] http://wjmc.blogspot.jp/2011/03/us-healthcare-costs-vs-life-...
Most countries use a variant of single-payer or mandated insurance for good reasons, the US was an exception, not because it has exceptional requirements, but for historical reasons.
https://truecostblog.com/2009/08/09/countries-with-universal...
I'm not sure how your link supports your point. the US spends far more on healthcare than the UK, but has lower life expectancy. Even if you remove private spending and only include government spending the US spends more on healthcare.
The US is a massive outlier globally. They have expensive, poor healthcare in comparison to the rest of the world. Compare any country to the US and that country will likely out-perform the US on most metrics.