Why read old philosophy?

Also, scientific methods and processes are based on theories and thoughts developed primarily by philosophers.

So when I argue that "the ancients were right," it would be more correct to say "some of the ancients were right." They cannot all have been right, since they disagreed with each other! Thank you for pushing me to clarify on this point. My deeper argument, though, is that it is impossible to arbitrate who is right from the perspective of the present. That is, it would be wrong to say that Aristotle or Plato is more correct merely on the basis of what is "in line with contemporary common sense." Of course, contemporary common sense could be right, but it could also be deeply flawed. Stepping beyond the confines of the present, and looking back to the ideas of the ancients, provides a helpful counterfactual for our modern way of thinking about things. It is precisely because the ancients were arguing about problems in a way that is different than the way we think about them today that they are worth studying. Not, again, to see who is more in line with the latest advances in our current understanding of physical, cosmological, scientific theory, but rather to help reframe the very terms of debate in which those theories work.

You hit the nail on the head when you observe that there are "bizarre passages" in ancient philosophy that "make us wonder what could have motivated the question at hand." Exactly! Your very confusion on this point proves that the whole question that Plato was addressing in the Cratylus has been forgotten in modern times. Of course, from the perspective of contemporary linguistics, obviously Plato is wrong to suggest that onomatopoeia has a conceptual basis. But is that all Plato is arguing in that text? It is precisely the framing of his inquiry in the terms of modern linguistics that does a disservice to his original thought. Indeed, the very fact that the exact nature of his question has been lost, as you point out, suggests that he may have been exploring a whole separate area of inquiry.

To be sure, by returning to such an area of inquiry I don't mean to say that "philosophy ended with" the ancients. Not at all! Philosophy is not something that has an end [0]. It is, rather, a way of living in the world -- a way of being perpetually open to ideas and therefore living the best life possible. But even if it did end in some fashion, I would never argue that it ended with the Greeks. It may have started there (though this is debatable), but the Greeks only represent a sort of waypoint -- certainly not the end all, be all. The goal of the student of ancient philosophy is never to return to Plato in order to, say, reinstitute the Athenian polis today. That would be stupid. Rather, the goal in returning to Plato (for example) is to understand the precise nature of the problems he encountered, in order to then return to that point and make progress from there. This is necessary because that starting point has been covered up by modern philosophy -- it has taken a wrong turn, as it were, and has closed down other avenues worth exploring. In order to recover those avenues it is necessary to return to their original point of departure, and to take them seriously as viable alternative, not simply as wrong paths that have been "proven" erroneous by contemporary advances.

Finally, since we are talking about Plato and Aristotle, I would also just mention that it is dangerous to say "Plato said this" or "Aristotle said that." This is because Plato wrote dialogues, and always presented his apparent positions through the mouthpieces of his characters. Aristotle, too, wrote is a dialogical fashion, often couching his apparent arguments in a response to the prevailing doxa (opinions) of the time. It is difficult, therefore, to ascertain precisely what Plato (the person) or Aristotle (the person) really believed. They also contradict themselves all the time -- Plato, for example, presents his political teaching in two texts (the Republic and the Laws), which are quite different. So while he may (may) have advocated for a communist regime in the Republic, he does not do so in the Laws. Obviously this provokes confusion on the part of the reader. What did they really think then?!? However, I would say that, again, it is precisely this frustration that points back toward another way of "doing" philosophy. Today, contemporary philosophers only ever write treatises, with precise, logical arguments. (Especially in the analytic school.) But Plato shows that there are other ways to seek and present knowledge. Remembering that is itself a worthwhile reason to return to the ancients as well. (And, incidentally, the reason that the author of this post gives, though on a slightly different rationale.)

[0] Though this claim is highly debatable, I should say. Hegelians would disagree. (In this vein consider the popularized "end of history" thesis advanced by Francis Fukuyama.)

I don't think that's really true in general. Sure, Plato is more approachable than Wittgenstein, but I don't think the comparison works the same with, say, Rawls in place of Wittgenstein.

Completely agree - I find my philosophy degree being most useful in what you've laid out and also in empathizing (or at least understanding) with what someone else is saying, especially if that person is bad at communication or cannot express themselves as clearly as they'd like.

The older philosophers tended to take the reader on a mental journey / through a mental exercise, and not always a clear one, so you're forced to extrapolate what's important from what seems to be nonsensical stream of consciousness.

I come across folks at work all the time who can't really explain what they're saying, but I'm able to extrapolate based off a few key words / phrases. It's a valuable skill for product discovery / design.

Caveat here is that one can develop the above skills without philosophy so it's not a requirement to read old philosophers, but rather one path among many.