The problem, it seems, is that the question presupposes conditions that are antithetical (at least on the surface) to the mission of the arts in the modern world. If we first stop and ask if the goal of education is in fact to "produce greater professional competence or higher salaries," then we could more directly or easily decide whether the arts are really worth (monetarily) investment of educational dollars. Assuming for the moment, that education is not about a material standard of living, but something more like the quality of life pursued, then quite obviously the arts or integral to such a revised educational goal. If, however, we as a society look only for the short-term gains that are appreciable only in tangible ways (even to the point of determining how many tourist dollars will flow from a new museum), then the arts will be forced to serve a purpose beyond themselves and become servants to an end not of their or their creators' determination.
Historically, of course, the arts have always served some master beyond themselves. The question is, should higher education do the same?