First, Musixmatch is easy to use, because it offers public search API with highly accurate results. In contrast Lyrics Translate is really unfriendly towards programmatic use and would require scraping.
Another is that Musixmatch is working with publishers and they often have lyrics available for a fresh release the moment it goes up — even if it lacks translation, that is already an added value. Lyrics Translate is community driven and it's up to a volunteer to first add the original lyrics, then to often another volunteer to provide the translation. Sometimes that process takes months if not years.
This leads to the third reason. Reddit archives posts older than 6 months; after that time you are no longer able to submit new comments. You can still edit them, but I don't want chrobot to make placeholder posts for possible future use, as that would be annoying to visitors. (This rules out replacing Musixmatch with Lyrics Translate.) Having that in mind, support for Lyrics Translate would pay off primarily for submissions of older songs.