I'm not sure that understanding this is that predicated on cultural familiarity. I'd argue the majority of its meaning comes from the fact that it "breaks the rules in order to be overly brief." The syntax being intentionally wrong, bad, and clumsy coincides with the fact that it's often used to describe absurd things and situations. Clumsy syntax = slightly belligerent rhetoric? I could be wrong, my main idea of a idiom is a proverb or figurative parallel illustrating a concept.
I don't think it's belligerent or simply compressed. AFAICT, it warns the listener that a lot is being left out. It is, in fact, the independent phrase version, using a single noun as the independent phrase. This tells the listener to deduce the rest of the phrase. The verb and object are generally omitted for reasons other than brevity.
"I added bacon to my ice cream because bacon" [is the most awesome thing ever] (and if you don't already know that or don't agree, I don't want to try defending it).
"The project failed because politics" [generally causes everything to fail] (and if I start talking about that I'll start ranting and no one wants that).
"Root beer in a square glass is beer because math" [uses "square" and "root" as opposites] (but if I said that explicitly it would harm the humor of the joke).
Contrast "I added bacon to my ice cream because of bacon", which would suggest that everything you need to know is there and it is the nature of bacon to be added to ice cream.
Off-topic, but just wanted to add that the four comments above exemplify why I still find hope in HN discussions. Each one adds some new insight, refining what was said previously and does it in a constructive way.
There's also ambiguity. I didn't think math was funny just because of the pun, but also because of the way people use math to justify homeopathy. It's mathematical, so it must be true. From a similar cultural perspective, I can see something totally different but also valid.
Most popular memes have cross-cultural appeal, and we each add to them.
