In comparison, my mother language is Spanish, a language with very simple spelling rules. My girlfriend is always surprised how she can read out loud a random Spanish text and even though she doesn't understand it, I will understand her easily (it also helps that both languages have very similar sounds).
(For the reader, Japanese has a lot of homonyms since it has a comparatively limited set of phonemes. Specifically a problem in writing due to lack of context, spaces and lack of tonality that can help disambiguate the language when spoken)
So the most obvious solution would be to drop on'yomi (Chinese readings) and go to pure kun'yomi (Japanese readings) whenever possible. My understanding is that such a strategy was used by the Koreans to replace Hanja with Hangul.
Now, I understand that it would be a massive undertaking and extremely unlikely to ever happen, and honestly it's not really my problem, so I am just speculating here xD
The obvious way people handle it in speech is by picking words that are clearer in context when homonyms might cause confusion. If you consume any Japanese video content on YouTube etc, it’s very common for speakers to say a homonym, instantly notice the ambiguity, and restate it using a clearer word or brief explanation, which they could, at least in theory, do in no- or low-kanji writing too.
同音異義語の区別に不可欠な漢字の廃止は不可能か?(Is abolishing kanji -- which is essential for distinguishing homonyms -- impossible?)