In Korean, it works similarly as well though, most people nowadays are quite used to not incorporating Hanja in sentences over multiple decades, to the point where it would be impractical to mingle Hanja in Korean.
Which is what every language with an alphabetic writing does, and it works just fine. It is not "another layer of cognitive load", it is just a different layer, one that can be said to be much lighter or other languages would not have switched centuries/millenia ago.
The real problem of Japanese is the massive amount of homophones coming from Chinese. It is already a problem in Chinese, but even worse in Japanese due to the smaller phonetic repertoire.
So you're saying that verbal communication doesn't work in Japan and everyone just texts each other? "I'm sorry Mr Honda Kawasaki but due to how Japanese language works it's impossible for me to tell whether you want to buy three oranges or cook prostate cancer, please send me a letter" "Okay I will fight the sky colander"
Most countries at some point had to simplify their languages in order to promote literacy. Korea didn't ditch hanja just for shits and giggles, it did so in order to make it easier for schools. Japan never really had to face this problem at a scale that required complete removal of kanji because by the time people got such ideas Japan was already quite literate, so kanji stuck around. Plus, Japan is an extremely conservative society, they only ever change anything once all other options have been exhausted.
Same reason why English spelling is so ridiculous. It's not that English is such a unique language that it absolutely requires a spelling system that doesn't make sense and effectively forces everyone to memorize each word's spelling aside from it's pronounciation (wow just like kanji), it's just that English spelling has never been a problem to a degree that required a systematic solution, so now we're stuck with what we have. If we suddenly decided to make a giant reform of English spelling to have it reflect actual pronounciation, the resistance would be equally giant.
I actually live in Japan, I am trying to learn the language, and it is royal PITA. Heck, every single Japanese person I have asked has complained about their language being so ridiculously difficult. They wish their language was easier, but as you say it is also such a conservative society that it will never change.
In comparison, my mother language is Spanish, a language with a highly phonemic spelling. My girlfriend is trying to learn it, and she always commends how once you learn a few basic rules, you can read anything.
Disagree. Once you get accustomed to reading kanji, and did not learn to visually parse (except very briefly as a young grade school child) nearly all of the words that you see regularly as logograms first, and groups of sounds second, the experience would be akin to reading English while afflicted with a strangely selective amnesia hole for entire words. Such that reading a word like 'shoe' would not instantly evoke an association with a piece of footwear but would have to be (admittedly very rapidly) sounded out letter for letter each time, instead of scanning the entire unit as a whole.
That's what reading a word normally represented by a familiar kanji character but "expanded" into hiragana feels like, and slightly more pronounced if it's, for some hipster reason, written in katakana.
And how many years does it take to? What about words that you have never seen before? What about ambiguous or uncommon readings that require furigana even for fully educated adults?
As I said in the sibling comment, I live in Japan and every Japanese person I have met complaints about the massive effort it took them to learn how to read and write.
Hangul has some funny rules around patchim that need to be memorized. Kana does a great job avoiding this, so on balance kana is probably just fine compared to Hangul.