But the greatest increases in life expectancy were from the late 1800s to the mid 1900s. The improvements have slowed since then, appearing to plateau in the last decade or so.
And it just so happens that in that time period, the government had way less control over the healthcare system in the US.
Literacy is actually decreasing in recent years, as education spending by the government increases. Higher education has never been more expensive, thanks to guaranteed student loans provided by the federal government.
If you're more talking about developing countries, then the correlation is far stronger with level of economic development than with government involvement. In fact government involvement is often inversely correlated, slowing development.
Don’t confuse government causing a increase in government spending on something with causing an increase in the actual supply of that thing. When governments restrict the supply of healthcare and housing (which they do, through professional licensing and zoning regulations), they can spend more on them without increasing supply.
You seem to not address fraud in the market, like snake oil salesmen, at all
The government caused all those things to go up