The main reason we had rules to force kids to attend primary school was to make obedient soldier citizens to support their nation in time of war.
Maybe. But that isn’t exactly what the study says. The study finds a correlation between “large investments in state primary education systems” and “military rival[ry] or threats.”
Aside from the usual caveat about correlation not being causation, I would add that it’s not especially clear that, were that it’s intent, the pro-war faction is getting its money’s worth. As near as I can tell, the purpose of public education is to promote Diversity and Global Warming, and I be greatly surprised to find public schools actively encouraging support for war. Once upon a time, subjects like, say, the history of America’s past military glories might have had second order effects encouraging support for the wars of the present, but these have now taken a back seat to Sojourner Truth and the Tuskegee Airmen.
I suspect that, if anything, the causality runs the other way, at least in the American context: it was precisely the experience of various wars that consolidated nationalism, making national expenditures for things like education more likely.
Elsewhere, Robin asserts a similar purpose behind nationalize health care. My guess is that such will bankrupt us to the point where foreign war becomes unaffordable.