A recent post by Amod Lele (http://loveofallwisdom.com/2009/06/neither-career-nor-hobby/) has the advantage of putting the question of the use of what we (=students and scholars of "unuseful" subjects) are doing in its right terms. One can also see a comment about a similar dilemma in the field of art (http://haikujaguar.livejournal.com/640442.html).
Through a degree and then a PhD in Sanskrit, one does not learn any "professional" skill apart from those required to keep on studying and researching in this field. So, since it is hardly the case that the number of professors/research fellows etc. in Sanskrit need to increase, why should one study Sanskrit (or Latin, or History of Dance, or Theory of Cinema, or Moral Philosophy…)?
One could suggest that confrontation with other cultures, critical thinking, sensibility enhancement (as the one one achieves through reading poetry) all contribute to one's formation as a better person. But what does this mean? In which sense is one "better"? Is one happier? Is one nicer to others? I doubt that the first answer can be answered affirmatively. One does not become happier through enhanced thinking and feeling abilities (often, the opposite is true, as underlined by Wittgenstein). Personally, I am suspicious about all kinds of philosophy as "consolation" (they seem to me to narrow down the potentiality of philosophy).
On the other hand, it is probably true that one who likes to get into philosophical/artistic/theoretic… problems is happier to do it than not. If Aristotle is right, and we all aim at knowing, then it makes sense that studying makes us happier.
But does it make sense to propose Sanskrit (or the rest) just as an interesting subject, or does it have in itself a specific value? This brings me back to the second alternative. Studying Sanskrit may make people better insofar as it increases one's understanding of other people's views. But this is hardly a satisfying reason for making critical editions of obscure texts or producing the translation n.1876 of the Bhagavadgītā. One can translate it for one's own sake (it is such a wonderful text), but it is hardly the case that one's translation will improve other people understanding of the text (see my previous "In praise of reading" post about my skepticism on writing before/without having read –and there are too many translations of the BhG to read them all before starting a new one).