There's an important distinction between ancient history and Classics, and it's one occasionally brought up in that thread. "Classics" as the study of important Greek and Latin literature might be dying in many places, but so are many other fields that have isolated themselves from a broader academic context. The literary idea of Classics is a dated concept from the early days of liberal arts education. There may not be many people going into it, but then, it can't (and never could) support many people in one field. That it should be a different department is unsustainable outside the largest schools.

My experience with "Classics" is very different. While my major did require proficiency in Greek or Latin, it also required exposure to all kinds of Greco-Roman studies. At my school's faculty, there's historians, art historians, archaeologists, and your traditional Classical Latinists/Hellenists. This group of people is constantly undertaking cool research. If you're not afraid to get your hands dirty with a little art or archaeology, you'll be fine.

u/Daeres puts it well in in one of his comments: he's an ancient historian who needs archaeology to get by. This is particularly true for Classical Greece, but still applies to Rome. For periods so far in the past for which we still have writings, it's tempting to choose history or archaeology, but the two must depend on each other to maximize our learning. There's not quite enough left written for it to stand on its own, and overlooking Latin texts in a excavation is foolish.

So even if the literary Classics were to entirely die out, the texts would still remain, and the ruins would still lie under the earth for you to study as a historian.