I understand this is partially supported by Nietzsche, but do others agree or adamantly disagree with this position? If so who?
One main thinker with this point of view is Kant, who argues in his Critique of Aesthetic Judgment that one of the main defining characteristics of art is that it has does not have an external purpose --a point of view agreed with by (among others) William Kennick in an influential essay otherwise critical of traditional aesthetics called "Does Traditional Aesthetics Rest on a Mistake."
However, this position is actually a more recent innovation, with older thinkers such as Plato and Aristotle taking it for granted that art played a specific function in human life.
EDIT: I should clarify, based on the comment below, the argument being advanced by Kant and Kennick, among others, is not that art cannot be devoted to external purposes, but that serving such a purpose has nothing to do with what makes it art.