Well, you can actually make a pretty good objective case for Japanese writing being the most complicated writing system on the planet, since no other language that I'm aware of regularly mixes 4 scripts, where basically entirety of Chinese forms just one of those scripts. Except that whereas in Chinese it's rare for a character to have more than one or two readings, in Japanese there are characters with over 70：
It's telling that there is what's effectively a reading test for Japanese people, where it requires 12 years of schooling to take a stab at Level 2 (covering only the "daily use" kanji!), and Level 1 requires years of additional study on top of that:
You're presenting this very misleadingly. Kanken 2 is basically comparable to something like an SAT; it covers what people are expected to have mastered by the end of high school (reading and writing, incidentally). As such it's odd to say it "requires 12 years of schooling" as if that proved something about the language.
Kanken levels beyond 2 are a different matter; they cover words that aren't in common use, and are more akin to learning trivia for the sake of learning trivia.
Most kids learn to read & write the alphabet in grade 1, although mastering the idiosyncrasies of English spelling takes a bit longer. By comparison, Japanese kids are still grinding their way through the jōyō kanji all the way to grade 12. So, yes, I think this tells you a lot about the complexity of the writing system.
Japanese kids learn to write hiragana and katakana at similar age which is comparable to the Latin Alphabet. By comparison, most English speakers still participate in stuff like spelling bees and have to actively learn to spell individual words (remember, English is not a regular phonetic language) well into adulthood.
Again: kanji tests are vocabulary tests, not just orthography tests, so Kanken is not comparable to first-graders learning the alphabet. If you're familiar with Japanese you must already know this, so I'm not sure what you're trying to argue.
The Kanji Kentei is not a language test, but specifically a test about kanji, and the fact that you need to be familiar with Chinese poetry etc to ace it showcases how complex the writing system is. About the closest English gets is asking obscure loanwords in spelling bees.
So like reading the original unadapted Don Quixote in Spanish. Not bad as Shakespeare, but some words had a different meaning back in the day, with inusual metaphors impossible to know unless you were an expert on Middle Ages.
For example, "La negra" would mean "the sword", and "duelos y quebrantos" wouldn't mean "mournings and breakdowns", but some kind of dish made by mixing scrambled eggs, chorizo and bacon.
Japan definitely has one of the most complicated writing systems in the world, but you can get pretty complicated with alphabets if you just go too long without spelling reform. Look at the split between Tibetan as written and Tibetan as pronounced, or basically anything to do with English and our complete lack of spelling integrity.
https://en.wiktionary.org/wiki/%E7%94%9F#Japanese
It's telling that there is what's effectively a reading test for Japanese people, where it requires 12 years of schooling to take a stab at Level 2 (covering only the "daily use" kanji!), and Level 1 requires years of additional study on top of that:
https://en.wikipedia.org/wiki/Kanji_Kentei