I wouldn't blame this on specialization, per se. This is more like asking why aren't critics good at sports/music/whatever. "Empathy" with the subject of study

I wouldn't blame this on specialization, per se. This is more like asking why aren't critics good at sports/music/whatever. "Empathy" with the subject of study to the point of total mimicry is or isn't part of the job description on a different axis. The trend in modern social studies to emphasize "historical specificity", or an impossibility of fully embodying living some other context, might provide some cover to those that don't learn the language fluency, but this point didn't come up in the original reply or your comment. If we want people to learn ancient languages fluidly, I think the right model is not even Academia, but, say the Europeans subsidizing rural quasi-traditional farmers for cultural reasons. Or "historically informed practice" in old music. It's not scientific study of the past, but an art or cultural practice in its own right. A good question to ask is how well the Romans could speak 500 years prior Greek. (Older forms of their own language was already covered.) That was also an cultural practice of reverence.