Like, I know someone who got a degree in Classics and the core curriculum seems to be reading and translating Greek + Latin + a modern language, either French, German, Italian, or modern Greek.
Example course:
"Roman Invective and Verbal Abuse
An exploration of the world of Roman verbal assault. Readings in Latin will range from inscriptions on sling bullets and walls, to scurrilous pamphlets, to formal full-blown invective speeches. We will investigate especially how themes within Roman invective reveal broader cultural values."
"The Roman Novel
Students will read substantial portions of the two surviving Roman novels, Petronius’ Satyricon and Apuleius’s Metamorphoses (or Asinus Aureus). In addition to improving reading speed and ability, the class will introduce the genre of the ancient novel. Students will be assigned secondary readings relating to the novels and will be expected not only to translate, but also to give oral reports on assigned topics and provide commentary on designated sections of the text."
You also concentrate in literature, archeology, or history.
You're right that Junior and Senior classes then learn more and stop worshipping just at the feet of Greek and Roman statues. That's a good thing. Education is more than these two cultures ad nauseam.
Point still stands, it's a decent overview, and I'd really like college students to go for breadth, not depth. You want to deep-dive, go get a PhD. (Or read on your own, it's cheaper that way ;)