Everything written in ancient Greek that is foundational to western literature, has already been translated, likely to a higher standard than most of the people trying to learn it.
Unless you wish to be part of an effort to further improve the quality of these translations, including to adjust them for the fact modern languages themselves are a moving target, just read those translations.
Modern Greek, on the other hand, is a living language with new art and culture coming from it. I may not be able to write "a cup of tea please" without misspelling tea, nor pronouncing it so badly they reply in English (as per my user profile), but this is infinitely more valuable than knowing if the ancient Greek character inviting people over for a meal is saying the people will eat the meal or be the meal.
To be fair, there are nuances in the ancient Greek which are best brought out by some study of the language. The most frequently translated ancient Greek text(s) would be the New Testament, and even there you can see a lot of modern churches base their ideas on dubious translations.
I find ancient Greek not so helpful when it comes to etymologies. Some are helpful, but many are obscure or misleading. Climax comes from the word for a ladder apparently, and electron comes from the word for amber. There are stories behind both but they won't get you far. Any word beginning with psych- tends to relate to the mind, but the Greek means "soul".
Sure, but to the extent that the nuances matter to modern literature, they're documented. For Church stuff in particular, the erroneous translation is more relevant to a full Western education than the truth of the source material it was based on, simply because the culture came from the error; that αἰώνιος in ancient Greek means "age-long" matters less to understanding Christianity than that the theological use is "eternal", the latter of which you can get without ever learning a single word of Ancient Greek: https://en.wiktionary.org/wiki/αἰώνιος
I don't mean to deny someone's fun side hobby, if anyone wishes to get into the archeology of linguistics that's obviously fine and good for them, but it's not really a useful or necessary thing for a "full" education as claimed by the quotation:
> Ancient Greek is needed to get a full Western education, for reading some of our foundational literature properly.
I wonder if the ancients complained about μονογενής the same way modern people complain about "very unique"? But again, what I question here is if this matters, I don't think knowing the answer is necessary for a "full" education.
Wow, what a way to write off something "foundational to western literature".
I studied koine Greek with my dad. Today, I study Aristotle alongside half-a-dozen English translations (the latest, Adam Beresford's Ethics, is hilarious, "like Han Solo and Chewbacca, Achilles and Patrocles" in the notes; his Aristotle uses "Perhaps...but that's a bit off-topic").
None of the English translations is as convincing as knowing the original vocabulary. Many phrases and idioms are still obscure or debated. Why should the student not want to look behind the curtain?
Finally, there is something bracing about knowing the ancient grammar. Greek has features long-vanished from English.
You would separate students into those who never need to bother looking a bit into "foundational to western literature" and those handful who are on a PhD track. Eventually, nobody would grow up to be recruited into the latter.
Greek is famously a lot more specific about what love is (especially in a New Testament context). English smooshes a lot of barely related concepts together to form its idea of "love" which encompasses care, lust, parental love, romance, charity and a number of other things.
Unless you wish to be part of an effort to further improve the quality of these translations, including to adjust them for the fact modern languages themselves are a moving target, just read those translations.
Modern Greek, on the other hand, is a living language with new art and culture coming from it. I may not be able to write "a cup of tea please" without misspelling tea, nor pronouncing it so badly they reply in English (as per my user profile), but this is infinitely more valuable than knowing if the ancient Greek character inviting people over for a meal is saying the people will eat the meal or be the meal.