Well, most of what we call knowledge are intelligent guesses, which survive experiment. There's nothing particularly special with kata understanding. Some things, we are told. Some others, we observe, make hypotheses on and experiment, finding a predictive theory, which we then verify.
For katas is very often possible because they're relatively new stuff, made by human people, we know the general idea of application (combat), and we can to a great degree peel off the layers of misunderstanding and disinformation because we know pretty much when and how it began happening. To make an example, fantasy swords can be completely useless because nobody actually uses them.
The game of Uno is much more arbitrary and simple and would be much harder to decode from nothing (even though once one's got the key idea..). Occam razor's also helps: if one agrees that kata was born from actual, selective experience (in evolutionary terms), it would rapidly be reduced to the simplest form achievable with the means of the time.
To make another example, Champollion did it with far less for hieroglyphs, which nobody alive had been able to read for thousands of years. He did it by looking at patterns, using the knowledge he had of the rosetta stone, making hypotheses, validate them and then trying to apply them to stuff he hadn't seen yet.. and it worked.
In other words, the fact that many people don't have a clue of what the context of kata was, doesn't mean it's
not possible to know. It just means that not many yet take the time and effort to drop their preconceptions and trace the history we know of and take the consequences (sadly, the same happens in all courses of life).
And even if some do, the information is not yet disseminated enough yet to become
common knowledge.
Actually, often this process is actively countered, because there's already a "common knowledge" and not enough selective pressure to dislodge it (since combat is a very rare occurrence nowadays, so it matters little if interpretations are correct or not).
And finally, there
is a huge selective force - money - that pushes in the direction of keeping alive the current idea of context, which makes kata hard to understand.
Imagine commercial interests pushing for a completely different game than Uno but using the same cards, and lots of people invested in playing it. Even knowing the original rules, you would have a hard time getting them out.
In practice, once you realize karate is a set of ideas to deal with close-range confrontations (because these are the confrontations that happened, and still happen, for which we know karate was designed.. exactly like we knew that hieroglyphs were for writing, not just art), without requiring youth, incredible athletic skills and has to be relatively simple, you have most if not all of your context.
Then you observe the katas - as many as you can - and find patterns and ideas that seem to work in that context - where "work" means surviving an encounter with attackers by quickly disabling them. Then you deduce the principles - which must match what you have observed. Here we are aided by the Rosetta stone of texts, writing and direct and indirect comments of people who lived when the art was actually applied and under selective pressure.
Then you put katas and principles together and come up with ideas, putting them to the test, hard - meaning with multiple situations and levels of intensity. Most often only one will actually "work" consistently, in realistic conditions. If there's more than one, you keep looking at situations and find if one works significantly better than the other, or you can apply Occam's razor - if there's a simpler way to achieve the same aim, then the one you're looking at ain't it.
Sometimes one won't manage at all and then yes, that bit of kata is truly lost (that is, maybe until someone more brilliant comes along
) but most often you can.
It can be done, it's just that not many do it.