Okay, even if we accept the basic logic there uncritically, it's not infinitely good. For example, the 24th year of schooling is not a public good, because there's no plausible argument that the social benefits it provides are greater than the cost. What about the 20th? The 16th? At what point does it cease to be a public good?

(Hint, we have some attempts to answer this question, and it suggests that college is a private good with a value that is mostly in signaling rather than skill acquisition, and casts some doubt on whether high school really meets the criteria)