Specifically in the case of Japanese language, the current orthography highly depends on the use of kanji to remove ambiguities from a purely phonetic notation in either kana system.

As a side note, Korean language also used to be written with hanja (Chinese characters) mixed in with hangul (native phonetic alphabet). The shift from mixed hangul-hanja notation to pure hangul was gradual and the major contribution that made it possible was the modernized orthography rules that allows visual differentiation of homophones when written down while adding some complexity. It’s not perfect, but it works.

So, while many argue that kanji is essential to Japanese or hanja needs to be reintroduced in Korean for examples cited, I think the definitive reason is that the japanese speakers themselves doesn’t feel the overwhelming need to switch right now. If they chose to introduce a purely kana orthography and had enough funding and political will, that’s how they will roll.