Classics is the traditional solution to the latter and I think it's still a pretty good one, but now that we can't assume knowledge or Greek or Latin, any other culture at a comparable remove would probably work as well.

Um, the reason for studying Greek and Latin is not just because they're a far-removed culture. It's also because they're the cultures which are the memetic ancestors of the memes that we consider the highest achievements of our culture, e.g., science, modern political forms.

Also this suffers from the problem of attempting to go from theoretical to practical, which is the opposite of how humans actually learn. Humans learn from examples, not from abstract theories.