The classics have their place as art and as sources of prestige, but if you're looking to learn things there are usually better places to look.
It depends, of course, on what kinds of things you are trying to learn. And that is precisely what is at stake here.
You definitely don't go to the classics to learn science or technology. But is that all there is that is worth knowing?
And don't be too hasty in your division of "fields that make progress" and "fields that don't." Our knowledge of Ancient Greece, for example, has grown substantially in the past century, and there has definitely been progress in historiography--but that does not eliminate the need (or, more to the point, the desirability) to read the primary texts.
While I agree that the division between «fields that make progress» and «fields that don't» is hasty, there is a division, in all fields, between research and the object of study, and research tends to change while the object of study doesn't; the Pythagorean Theorem, for example, is still widely taught, even if it's not necessarily taught from Euclid's Elements. Similarly, while, say, Jane Eyre(I hated that book, but it's a good example) persists, today's criticism of the book is far different from that which was written when the Brontës were still alive.