Pay no mind to the Victorian style imagery- I use that primarily because it's in the public domain and easy for me to find (and I do think it's cute).
But make no mistake- this kind of education never goes out of style.
It's not old-fashioned just because it relies heavily on the great books that have been part of the great conversation since books were written. In volume six, Mason is giving a sort of general overview of the literature she uses. She explains that the reading for high school "is more comprehensive and more difficult. Like that in the earlier Forms, it follows the lines of the history they are reading, touching current literature in the occasional use of modern books; but young people who have been brought up on this sort of work may, we find, be trusted to keep themselves au fait (editor's note: that is, current) with the best that is being produced in their own days.
It is a modern education and a classical and old fashioned education in the very best sense of each of those terms. There's nothing out of date about it.