>A snafu is a general situation in a system where nothing works because it's chaotic, disorganized etc.

Not even close.
Some chaos and disorganization would have been an improvement.


Have you read Catch 22?
The late Joseph Heller understood SNAFU as few did.


One reason I saw for SNAFU was "time in grade."
That means that the longer you stay in a rank the more likely that you'll be promoted. Think about that. If you're not promoted, that makes you more eligible to be promoted, and you usually are.
So most of my sergeants were people who had been passed over for promotion so many times that they had to be promoted- and it showed.