I believe the argument was that they do contribute to a functioning democracy, as opposed to investment in training nurses and carpenters, who are being trained for economic reasons. The argument was that the two goals are so different that they should be funded differently.

Not at all, most of these are obviously "symptoms" of a well functioning society (not just democracy), not its cause.

Last time someone got rejected from art school, there was a bit of a fascism that happened, so investing in arts totally contributes to functioning democracy!