Allowing for just the possibility of non-financial rewards of an education shows how shallow our "return on investment" culture is. When we see no value in learning about art, philosophy, history...what does that say about our values?
The debate from their perspective is simply that you only seem to see value in learning about art in education if someone else pays for it for you, but not enough to pay for it yourself.
The question of "the value of your education" can never win the argument against privatisation/optimisation of education, because the more "value" there is the more the consumer ought to be willing to pay for it.
The reasons for keeping education largely public and unoptimised are outside of that -- avoiding competition on price (richest-student wins), that the lecturers have a by-product that is useful to society (mulling problems where we don't yet know whether they have value or not and the market cannot price them), getting students from multiple backgrounds to bounce off each other (avoid social silo-isation by discipline) etc.
It's a lot harder to deal with, but it isn't somehow excluded from the purview of economics.
It's probably even necessary to make economic considerations when it comes to education. Given limited resources, choosing to put them towards things that return more value probably makes sense.
You should really try to see this from a non-monetary, non-utilitarian perspective.
For example, if your desired outcome is self discovery, some education based on indoctrination probably isn't going to work very well. That's a silly example, but choosing between methods and selecting the one that best delivers the result you desire isn't real distinguishable from making an economic choice.
I don't know how to make you stop thinking in a utilitarian way. There are other philosophies, you know?
I responded to the juxtoposition here: There is no reason to apply economics to education. "Value" is not only monetary.
I'm not insisting that you view education through the lens of economics, I was pointing out that what you said about value was not an argument against economics (because economics doesn't care about what form value takes).
You keep looking for a word other than value to describe this thing that you think should happen because then I can't point out that you can analyze it economically, but this is not a way to argue that education should not be analyzed economically, it is a misunderstanding of economics (it was really clear when stated as "Value" is not only monetary, but "we should do it just because" is still an imputation of value...).