> So simply put, the USA was already a socialist paradise by the time they came to name their schools

Amusingly Marx in the Critique of the Gotha Programme, used the (then) US system of regulation of schools without running them as an example of a system preferable to state run schools (I realize you mentioned "state funded" as opposed to "state run", but in most state funded systems too it tends to be the state that sets the curriculum in particular and exercise far more control than outlined in the quote below):

'"Elementary education by the state" is altogether objectionable. Defining by a general law the expenditures on the elementary schools, the qualifications of the teaching staff, the branches of instruction, etc., and, as is done in the United States, supervising the fulfillment of these legal specifications by state inspectors, is a very different thing from appointing the state as the educator of the people! Government and church should rather be equally excluded from any influence on the school. Particularly, indeed, in the Prusso-German Empire (and one should not take refuge in the rotten subterfuge that one is speaking of a "state of the future"; we have seen how matters stand in this respect) the state has need, on the contrary, of a very stern education by the people.'

EDIT: Note that he does not argue against public/local government influence on the schools, but it is a red thread (..) in Marx' writings that he was strongly critical of state influence vs. local, direct control.