It's all solvable. Korean did it. Koreans are fine.
For verbs you could just replace the kanji with katakana so that you still get the pattern recognition of okurigana as a visual aide.
They just don't want to do it, because they don't like to change. A generation educated under a new system wouldn't have difficulty using it. They would however lose access to an abundance of cultural artefacts which play a central role in daily life.
Koreans don't seem entirely fine to me, but besides, Japanese pronunciation is actually more aggressively simplified than the other two CJK languages during Edo era that numbers of homophone is out of control.
There are as many as 50 homophones for koushou due to this, for example[1]. Communication by phonetic transcripts alone just isn't going to work.
I've spoken Japanese for the last 15 years. I'm aware of how many homophones there are. I still think by and large it wouldn't be a problem, and that natives would adapt to route around it. It's not a blocker.
For verbs you could just replace the kanji with katakana so that you still get the pattern recognition of okurigana as a visual aide.
They just don't want to do it, because they don't like to change. A generation educated under a new system wouldn't have difficulty using it. They would however lose access to an abundance of cultural artefacts which play a central role in daily life.