The healthcare sector is one of the most regulated and least private in the US.
The NHS looks good compared to the broken American system. But it's a spendthrift compared to Singapore.
Healthcare outcomes in Singapore are no worse than in the US or UK.
See https://en.wikipedia.org/wiki/Healthcare_in_Singapore for more information.
https://data.worldbank.org/indicator/SH.XPD.CHEX.GD.ZS?end=2... has the numbers. Picking 2019 to avoid covid's effects you get:
US: 16.68%
UK: 9.87%
Singapore: 4.42%
The world bank also has data to show private vs public health expenditure.