The Japanese-language wikipedia page goes into it in more detail: https://ja.wikipedia.org/wiki/%E6%93%AC%E5%A3%B0%E8%AA%9E
Abbreviation, repetition, and stacking bits of words together are a big difference between natural vs formal Japanese language skills. It's very Lego-like that way.
It has great illustrations that quickly get the idea across for Japanese onomatopoeia.
To give an idea of what it is like, here are a couple of example pages: <https://livedoor.blogimg.jp/akky_san/imgs/b/2/b21ad72f.jpg> <https://livedoor.blogimg.jp/akky_san/imgs/3/4/34cf6c82.jpg>
Quite fun to read!
I find it very similar to english though. Cows don't actually make a sound anything like "moo", and birds don't "chirp".
I think you're right on when you say it's cultural.
Another important thing that shapes these things in Japanese is just how old the culture is. So much is inherited from ancient times...
To this day I still discover new ones that constantly amaze me someone was able to put a sound to it. I think my favorite to date is probably mozomozo. My wife used it to describe a baby flailing it's arms around. I was like ok... What do you mean? She repeated the action of flailing the arms around. I laughed. Oh the Japanese.
Japanese isn't generally considered to have the equivalent of the 'l' sound from most other languages, and it rather has a sound that's perhaps somewhere between 'l' and a rolling 'r'. In romanized text it's generally written as 'r'. Transliteration isn't really unambiguous in the end, though, and there are multiple ways of romanizing Japanese, so while romanizing くるくる as 'kulukulu' doesn't sound like a very common transliteration, it may be possible.
Also, 'kuru' means 'to come', but I don't know if that's related.
English has a huge variety of terms for extreme tiredness: whacked, bushed, wiped out, worn out, drained, burned out, beat, knackered, fried, shattered, frazzled, zonked... must be the puritan work ethic or something.
We've even got a few onomatopoeia of our own: feeling kinda.. ugh.. meh... bleugh... I mean, whew, yeesh. Just... phew.
Maybe being tired is just the global human condition.