I think the main issue here is "accessibility out of context" i.e. how accessible is the raw emotion behind the event to someone viewing it with very little context to go on. The most immediate and easily accessible example of accessible emotion is the killing of Bambi's mother in Bambi, it's one of the most popularly referenced moments of movie sadness in the history of cinema and storytelling. You don't need much set up, Bambi had a mother, she was rather needlessly shot by hunters, Bambi was left alone and afraid in an unforgiving world. Everyone finds themselves feeling sorry for Bambi.
It's an aspect of storytelling that Pixar have managed several times most notably in Finding Nemo and at the beginning of Up. Essentially the context of the story itself provides all the information we need to feel the emotion. In Finding Nemo all we know is that an average father and average son lose their average wife/mother within the opening moments. Could be anybody, was just one of those things. In Up we know that two bright, spirited, normal people were very much in love and had dreams and that one lost the other and had a feeling he had somehow let her down. It's easy to see and relate to how that situation might occur to anyone at any time.
The difficulty with something like 9/11 is that the weight of the circumstance is such that it needs a hell of a lot of context to make it make sense. When you say to someone that someone flew commercial airliners into some of the world's tallest and most important buildings the weight of the event is such that you can't take it as a personal tragedy, it's too huge for one person to process all at once.
Where you can take a world changing event and make it timeless is when you have found that personal nugget that simultaneously marries the global with the personal. For example Julius Caesar's death would be too difficult to really comprehend until you boil it down to one guy who maybe went a little too far being summarily executed by a dozen of his best friends including his very closest companion: Et tu Brute?
Shakespeare, in fact, does several things in Julius Caesar which make that event timelessly tragic. He is careful to portray Caesar as ambitious but urbane and possibly reasonable; he might possibly be the best God-King Rome never had, he is portrayed as the perfect statesman rational, emotionally stable, charismatic and comfortable in power. Then Shakespeare drops in Brutus, quiet, thoughtful, considered, if he is Caesar's very best friend then that speaks well to Caesar's counsel. Finally, Mark Antony is here portrayed as the violently passionate young man who idolises Caesar. The vigour with which he supports Caesar and is outraged by the cold and calculated acts of the senate is infectious. His passion literally rouses the rabble.
What Shakespeare does is make all of these characters human. None of them are perfect, all of them are likeable in some sense. It is only Cassius who is a pure pantomime villain, snake-like and predatory. He gets to Brutus by appealing to the reason that Brutus is proud to possess, the turning of Brutus is pure politics and from there the rest of the events seem, somehow, inexorable.
Julius Caesar boils down the events upon which the Roman empire turned to a series of quite understandable human choices. Each piece in that puzzle is vital, and it comes down as far as making Brutus quite likable. If Cassius had been the clear villain, not requiring Brutus to do his dirty work then we instantly lose a whole dimension. In the final battles of Julius Caesar we understand the point of view of both sides, we understand why everyone did what they did and the real tragedy is that we can't see how people could have acted another way without significantly betraying their sense of identity. Of course, Cassius should have just shut his trap and kept his nose out, but we don't have to care about him so that's unimportant.
I think that this leads onto a final point. We understand why the hunters shot Bambi's mother (possibly less so in the modern era but still enough to make the tragedy), we understand why the big fish ate the little fish, we understand why Carl and Ellie put living a life before the childish dreams of exploration. We understand the whole situation and that's what provokes the emotion.
With 9/11 (and I come back to this because it's the example you give) most people would claim, and I have had arguments with people who have put this perspective to me, that we shouldn't want to understand or sympathise with what would make a man fly a plane full of passengers into a building. I'm not here to argue that case either way. All I will say is that when you can tell a story that stands for ages you do give everyone air time and you make it quite plain why it's a tragedy for everyone except the cold and calculating serpentine intelligence that lurks, Machiavellian to the core, in the shadows and whispers in the ears of those who would be tempted.
In my opinion until you can make the audience feel, or at least understand, all points of view surrounding an event the story of that event cannot be timeless.