You should not leave out the elite universities. They have been socialist seminaries since the 1930s. Their missionaries have taken root in the every cow college in America.
You are correct. Under John Dewey's stewardship of the Columbia University teachers' college, so-called progressive education, with its attendant emphasis on socialization (i.e., conformance with subjective social norms) and deemphasis on learning and basic learning skills like phonics, spread throughout the educational system. Many conservatives may sneer at the "ivory towers" of the prestigious universities, but those ivory towers are the control towers of intellectual life. Secular humanists and socialists gained control of these universities in the 1930s and even earlier, if you are talking about Harvard or Columbia.