A couple of points more central to the original post:
1) Primary and secondary education can't self-fund through research
2) Primary and secondary education can hardly be described as free. There is a strong minority fee-paying structure and for those that are nominally "free" parents and teachers effectively fund a sizable part of the operating budget through donating time and money.
3) The idea that an argument could be made as equally for primary and secondary education as could for tertiary is, frankly, absurd. For one, it ignores the indisputable fact that different levels of education are not independent. Tertiary education requires completion of primary and secondary education. It also ignores the fact that a base level of education (we can dispute where that level is, but it doesn't change the point) is a public good.
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