YouTube still allows uploaders to mark their videos as CC BY 3.0 licensed, and it's still possible to check that via YouTube's API.

(See https://support.google.com/youtube/answer/2797468 and the part about status.license here: https://developers.google.com/youtube/v3/docs/videos)

And the audio recordings are also curated by the volunteers, ensuring the audio snippets matches the text, etc.

Which, it must be said, isn't always as bullet-proof as it could be. There's a not insignificant amount of transcription (or pronunciation) errors in those datasets and Mozilla might want to find ways to increase the quality of already-released data over time.

Are you sure it's not fair use? I believe most legal experts agree that language models such as GPT-3 are not violating copyright due to fair use.

Fair use isn't a feature of copyright in every juristiction, which could make this a less than useful idea trying to create a global corpus of speech data.

Fair use is whatever a judge and/or a jury says it is.

Source?

This is incorrect. Pretty much every state of the art model uses copyrighted data. This is considered fair use and it has never been a problem outside of concern trolling.