Things are deemed "timeless" when people keep reading them over the generations. And your argument for why they should read them in the first place is that they're "timeless". That's circular.
As for "primary source", that's if you treat ideas as historical artifacts. If you're actually interested in the ideas themselves, a more apt metaphor would be learning obsolete technology. This is sometimes good, but not often. For example, I recently learned how Intel 8080 works, because I wanted to know more about how CPUs work, and modern ones were too complicated for me.
The themes/messages are timeless, not the works themselves. Here is my point: Would you rather read Plato, Aristotle, and the like, or the writings of a more "modern" philosopher who had conceivably based his opinions on all three?
And yes, using word timeless twice in my original post does make the argument appear circular. Works are not timeless because they are timeless (circular indeed!) but because their themes are timeless AND they were the first to thoroughly explore those themes.
OK, define "timeless" that way. It still doesn't follow that these things are worth reading. Being first doesn't make you best. Figuring out what's best is a very hard problem, of course, but it's a problem worth trying to solve, rather than giving up and going for the next best thing, which is prestige. Plato and Aristotle are good examples, because reading them is a waste of time (but very prestigious). See http://www.paulgraham.com/philosophy.html.
PG doesn't say that, not in my reading at least. If you're interested in the current state of philosophy, I think that's a great essay. But in it, I think the claim is that you need to read the classics to learn from their mistakes. That is, if you want to "do philosophy".
And while PG may be unsure of his influences, the more I read his essays the more I see serious traning in philosophy. He's meticulous in defining concepts and using them consistently. That's exactly the problem and goal of post-Wittgenstein philosophy. Sure, the ultimate utility of the field of philosophy is in question. But, to me, the endeavor has a firm role to play in the education of the mind. Math is more precise, but most of us communicate everyday by using concepts. In conversation, though, how do we make sure we're using the same (or similar) concepts with each other? How do we know we're consistent with ourselves in our own concepts?
The essay, you referenced, is "How to do philosophy". If you're going to do philosophy, the approach he proposes includes learning from past mistakes.
That said, I agree with his answer to the raq - you'll be better served by doing philosophy in other fields. Still, I think that's a big difference from saying those classics are a waste of time. In learning to abstract concepts, learning from previous struggles isn't a bad way to go. I am agnostic, however, on the best ways to learn how to abstract concepts.
As for "primary source", that's if you treat ideas as historical artifacts. If you're actually interested in the ideas themselves, a more apt metaphor would be learning obsolete technology. This is sometimes good, but not often. For example, I recently learned how Intel 8080 works, because I wanted to know more about how CPUs work, and modern ones were too complicated for me.