So at a minimum, dropping kanji would mean the language needed to develop a system for where spaces go (which is less trivial than it sounds IMO). But also it would need to abandon a lot of homophones or find some way to disambiguate them. It could happen I guess, but I'm not sure how it could happen gradually.
It's a bit easier for Korean as it has far more available syllables (so fewer homonyms), but you could easily imagine these languages making different tradeoffs and ending up in different places.
I think at some early point most Japanese learners (that don't already know a Chinese language) think kanji should be dropped. And at a later point I think most would change their mind as the advantages outweigh the disadvantages.
At least, that's the reason why I prefer still having kanji around.