Google Authenticator is actually one implementation of RFC 6238. That’s a problem for Google because:
They don’t control it: RFC 6238 is an open standard
RFC 6238 works offline, meaning Google can’t use it to track you and increase the surveillance on you
Google has been trying to kill off the Google Authenticator for years. Or rather, let’s say, gently push users away from it using dark patterns and promoting more convenient solutions.
Which is why everybody should use it as much as possible, because anything Google doesn’t want is bound to be better for the user. I mean I know TOTP is far from perfect and not super-secure if you’re a high-value target, but it’s good enough for most people and it keeps Google in the dark.
I wasn’t aware that Google uses the Youtube app as 2FA, but of course it makes total sense to them: it’s online and it’s one more surveillance point on your record whenever you use it. Then again, if you use Gmail and Youtube, there’s a good chance staying clear of the Google surveillance isn’t a priority for you, so it’s okay for you I guess.