Are Latin and Ancient Greek dead? Ostensibly yes. But not useless. Besides teaching, there is a tremendous amount of books and texts written in Latin and Ancient Greek. To study them, one would invariably need to learn the language.
Texts from the ancient world are handed down to us not from on high, or a single authoritative source (please consider the problem of duplication prior to computers or mimeographs), so considerable effort and erudition is entailed in comparing sources, filling in lacunae (here's a true warrant for what most consider a sesquipedelian word), all of which is predicated on perusing (in vain) an intuition for "pure et clare latine" and a hard-nosed insistence on _attested sources_ on matters of usage and expression.
I treasure, uncountably, the continuity afforded by training new generations in "antique" languages and dialects. It addresses a much deeper and more valuable problem than shitting out the next side-hustling platform.