Ever seen that episode of Star Trek: The Next Generation named "Darmok"? It's a version of the classic "Enemy Mine" story, but with a twist -- the aliens communicate purely in references to shared cultural heritage. In our terms, they would express tragic love simply by saying "Romeo and Juliette".
Have you seen a good collage video recently? Clips from a variety of shows are all smashed together, sometimes audio and video overlapped in ways never intended by their authors, with the occasional net effect of making a point unrelated to the individual shows, but expressed through their combination?
The quotes here are somewhere in between those two concepts. They're about quickly expressing an entire concept simply by repeating the words of a prominent proponent of that concept. We're not claiming that the concept expressed in the quote is correct because it was uttered by someone famous (say, Einstein), but rather the quote is available to us, and part of our shared cultural heritage, because its author was famous. We use it because we agree with it (for our own reasons) or find it worthy of debate, and so use it more as a shorthand for expressing some longer concept, not as an argument for that concept. Very few quotables are actually good at convincing anyone of anything -- they're just good at rallying people to a cause.