Is education a public good? Does someone else’s learning algebra or Shakespeare make you better off? Well, there are network externalities — in reading this you benefit not only from my learning but from that of anyone from whom I’ve learned. But I would guess that most of the benefit of learning goes to the learner, in enhanced earning power and in the ability to enjoy thoughts not available to the ignorant. (I’ve seen that stated as unsupported fact, somewhere or other.)
The question has many aspects, not all readily quantifiable, but at least it appears that spending on schooling is not correlated with economic health.
Worse, that enhanced earning power comes in part from a zero-sum game of signaling, at the expense of non-students.