There are incorrect reading or Chinese readings occasionally, but you can tell when that happens due to the furigana being different
But how do you know the furigana are correct? Unless you start out fully human-annotated text, you need some automated procedure to add furigana, which pushes the problem from "TTS AI picked the wrong reading" to "furigana AI picked the wrong reading."
It _is_ fixable though. It took me about a week, but I have yet to find a mistaken reading now. This also seems to just be the case with Japanese - most tonal languages seem to have the correct tones (I’m not qualified to comment on how natural the tones sound, but I have yet to find a mismatch like in Japanese)
I think Japanese is somewhat special though for a large number of homonyms (i.e. words that are spelled the same) so speaking with the correct pitch becomes somewhat more important.