Could one possible answer be that we still don't understand the plaintext behind the encryption? In other words, attempting various decryption seems to rely on the fact that you know what you're looking for underneath. You know what the end result should be.
The end result should be bits that are ordered and make up 1) some sort of filesystem and 2) files on that filesystem that are coherent as to be interpreted by something as intelligible data (e.g., something that a text editor, image viewer, or audio player could then interpret for you into words, sights, or sounds).
But... what if I did the following:
Now you use whatever tools you want to "decrypt" my drive. Imagine you are able to identify my algorithm and even my actual password. Groovy; but now you go about studying the data and begin vigorously banging your head against a wall. Why doens't it make sense even though it's decrypted??
Perhaps bad analogy. My suspicion is that unless we both successfully decrypt and know what we were looking for, "decryption" wouldn't help make the underlying information any more intelligible, even though nature doesn't destroy it's patterns.
After a re-read just to make sure no "stupid-alarms" went off, maybe I don't understand the "???", either. I guess the other examples struck me as cases where we do know what we're looking for -- some correlation, a difference between a control and experimental group while varying just one thing between them, watching objects to see what they do and how to describe their behavior using set values.
I took the last box to be "how do we run advanced decryption on the remaining unknowns" and I'm saying that it might come down to knowing what we would be looking for if we successfully decrypted the information before using those techniques would be useful. And this seems like the case in the rest of the examples.
I wonder if it is even meaningful to ask what the 'plain text' might look like.
Suppose we somehow managed to decrypt the universe and obtain its Theory of Everything. Then we notice that there's a pattern in the Theory which can be easily compressed (maybe a repeated constant bitstring). Wouldn't we then appeal to Kolmogorov and say the 'real' Theory of Everything is the shorter program which generates our larger Theory with its repeating constants?
And so on, for all the patterns we find, until we wind up with a Theory which looks like a substring of Chait...
Short version: Why can't cryptanalysis methods be carried over to science, which looks like a trivial problem by comparison, since nature doesn't intelligently remove patterns from our observations? Or are these methods already carried over?
Long version: Okay, I was going to spell this all out with a lot of text, but it started ballooning, so I'm just going to put it in chart form.
Here is what I see as the mapping from cryptography to science (or epistemology in general). I want to know what goes in the "???" spot, and why it hasn't been used for any natural phenomenon less complex than the most complex broken cipher. (Sorry, couldn't figure out how to center it.)
EDIT: Removed "(cipher known)" requirement on 2nd- and 3rd-to-last rows because the scientific analog can be searching for either natural laws or constants.