I was recently just playing around with Google Cloud ASR as well as smaller Whisper models, and I can say it hasn't gotten to that point: Japanese ASRs/STTs all generate final kanji-kana mixed text, and since kanji:pronunciation is n:n maps, it's non-trivial enough that it currently need hands from human native speakers to fix misheard texts in a lot of cases. LLMs should be theoretically good at this type of tasks, but they're somehow clueless about how Japanese pronunciation works, and they just rubber-stamp inputs as written.

The conversion process from pronunciation to intended text is not deterministic either, so it probably can't be solved by "simply" generating all-pronunciation outputs. Maybe a multimodal LLM as ASR/STT, or a novel dual input as-spoken+estimated-text validation model could be made? I wouldn't know, though. It seemed like a semi-open question.