Japanese doesn't have tones, it has pitch accent, and pitch accent applies to words, not phonemes. You would have to invent a system where pitch accent could be indicated for each word. The difference between 橋 (bridge) and 箸 (chopsticks).. the pitch accent is slightly different. But written the same in Hiragana: はし So there would have to be something (wavy line above the text?) to indicate pitch accent. Not sure how that should be done. And then there are the words with little or no pitch accent difference, only context.. in kanji they're different, would be the same in hiragana, so how do you encode that.. compromises would have to be made. I'm sure people have tried to come up with something, somewhere. Maybe.
But then again.. it's that other problem: Reading when there's kanji is much faster. Even for beginners. If you don't understand a word in kanji then it doesn't work, but as soon as you understand it it's way easier and faster to read.
> You would have to invent a system where pitch accent could be indicated for each word
Really not hard to do. A symbol on the syllable bearing the pitch accent would solve the issue
> And then there are the words with little or no pitch accent difference, only context
What's happened is that effectively a written "shorthand" has emerged that has evolved somewhat separately from how people speak. Losing kanji would mean losing this shorthand, in favor of writing more closely akin to the way people actually speak, but this is how the vast majority of written languages work. Preserving this shorthand seems like thin gruel to justify the complexity of kanji.
Pitch accent is not accent as in English, it's not any "the" syllable. If you've ever seen any of those videos about it, you'll see these down-up-flat patterns over the whole multi-syllable word. From high to low, from low to high, or low to flat plus/and other variations.
I wouldn't compare kanji to shorthand. Shorthand is typically not easy to read, normal writing is easier. Reading written, fully-spelled English is fast. Reading hiragana is slow (and I've been reading hiragana for a long time)- it's slow, and mentally much harder than reading with kanji. The only issue (and that is of course an issue, but tiny compared to Chinese) is that there's a lot to learn before everything can be read fluently. But reading only hiragana is just.. too hard, for any serious amount of text. It's not hiragana per se, it's the language itself with its limited set of phonemes which contributes to the difficulty.
Pitch accent in Japanese is deterministic based on the mora that is "accented". While it's true the effect of this accent "spreads" across the entire word, you only need to mark a single mora to know the effects word-wide.
> Reading hiragana is slow (and I've been reading hiragana for a long time)- it's slow, and mentally much harder than reading with kanji.
What's the ratio of hiragana-only text that you read compared to Kanji? And does the hiragana text uses spaces between words? My strong suspicion is "low" and "no", respectively. Familiarity breeds comfort with any writing system, and word breaks are a fabulous ergonomic tool for easing reading.
When I started Japanese a long time ago I would read (small) children's books because all I could read was hiragana. With spaces, for the smallest children. And that was all I read and could read.
And yet.. as soon as I could read various words with kanji, the reading got easier and faster.
> I'm sure people have tried to come up with something, somewhere.
Perhaps related is the abjad used in Arabic and Farsi. Vowels are written with diacritics above or below the main part of the character, which represents a consonant. However, in modern Arabic, the vowels are rarely written and are inferred from context.
The bigger problem for Japanese is the absence of spacing between words. Even if you write everything in hiragana with spacing, it's significantly slower to read than when kanji is present without spacing. The mixing of kana and kanji usually provides a hint as to where word boundaries are, because there are few cases where kana is followed by kanji in the same word (eg お and ご), and kana which follows the kanji are most often a continuation of the word (okurigana) or a particle. Some words are usually written in kana despite having kanji available, and their presence can sometimes make it more difficult to read because they might look ambiguous with a particle or okurigana, and you have to figure out from context what was intended, which slows down reading slightly.