Enough is being invested, it is just being spent extremely poorly. No country gets less per dollar on education than the US. A good start would be supporting school choice so the public school's monopoly and cost structure can be challenged.
I think the only well known non-US private school system (off the top of my head) are UK commonwealth secondary boarding schools, and those schools are more well known for their abuse than their academic strength.
Pretty much any other country (for example, France, Japan, China, etc) are generally built on a system of publicly funded schools
Private for-profit schools can use their money to get political influence and reduce public school funding in order to further its economic advantage.