"Actually, the system began to rot from within when atheist/socialist John Dewey became the dominant influence in American education. The reading methods were sabotaged, resulting in ever-increasing illiteracy until the rate now hovers around 40% to 50% and higher in some school districts. Every child who can’t read becomes a low-information voter." Yes, this is true. But his influence didn't begin to assert itself until the early 20th Century. Locally funded and controlled schools began with the first colonial settlements, so there is a lengthy period of time in which said public schools work just fine. Many of them were initiated by religious groups, true....but they were still locally funded and controlled.
The real death blow was "desegregation", in which courts basically took over many schools or placed them under (ultimate) federal control.
**Modern** K-12 schooling has its beginnings in the mid-1800s when states enacted its compulsory attendance laws and laws for compulsory and single-payer funding.