I disagree for a couple of reasons. First, Latin and Greek didn't die because they have nothing in common with Mandarin. English is the universal language, and it has nothing in common with Mandarin. Also, that there are modern concepts that can't be expressed in Latin or Greek is of no consequence. This was true for English monks in 1650. Latin and Greek evolve in use, or are combined with other languages to overcome this problem. English also had no way to express concepts like "transceiver" or "RADAR" "esprit de corps" until we needed a way, and now we have one. So it is with Latin and Greek. Reading classics, of course, can be done in any language. We read Tolstoy in English, why not Plato? This was not a reason to use, or to abandon Latin or Greek. Performing well on the LSAT could be influenced by the study of Latin. If it helps you deduce the meanings of only a few unfamiliar words, that could be the difference between a score of 166 and 174, which is not small, although it's true that the studies you don't do while studying Latin might be more useful, so I agree it's sideline trivia.

I think the reason Latin and Greek were prominent was that they were the languages of the powerful churches. They were the languages of the powerful churches not because of scholarly value, but their political value. By doing religion and scholarship in any foreign language, it can be made exclusive to a class of people chosen by the churches to study that language, and out of the hands of everyone else. The upper class becomes more powerful if they have exclusive ability to decode information that the peasants can't. Peasants are then dependent on priests for salvation because they can't learn that god never actually said priests should own all the land in the village. They are forced to believe the magical priest who can read the magical books. When this condition changed (think of Martin Luther), the legacy of Latin and Greek remained. A peasant could rise in class by learning it.

Latin and Greek died with the Industrial Revolution when British, American, French, German, and Russian (the colonial powers) educational institutions changed from places of scholarship and religion to places to train the masses to serve commerce.

Think about this. When schools are criticized today, it's almost never that they fail at religious (or state) indoctrination, (although lots of people want Jesus in schools) and rarely that they fail at scholarship (although some people want more art), it's almost always that they fail TO PREPARE KIDS FOR JOBS! Kids don't need Latin to work on the Boeing assembly line! Kids don't need Greek to become actuaries! When an American school has a budget windfall, they don't spend it on a new human rights studies course (the modern equivalent of the priesthood), or a new African history class (scholarship), they combine it with a grant from General Dynamics to develop a robotics program because the General Dynamics executives have been screaming for years that because schools are not using tax money to train their workers for them, they have to spend their own money to train their own workers, and boy are they pissed! And parents love the idea that their kids will find jobs with General Dynamics. And kids love the dream of that fat General Dynamics pay packet and all the video games they will buy. So fuck human rights studies (public service) and African history (scholarship), what we want is to get a piece of the corporate pie.

Latin and Greek were prominent because they were useful to the masters (churches). They died because the new masters (commerce, corporations) don't need them.