Lack of loyalty is a really good point I didn't think of. UUG2 seems like a progressing idol group so it's not like she would be changing groups to stay relevant.
There is another angle you missed. Tsunku is now working with UUG2, why would she want to leave that
The content license in the video is set to Babymetal's channel with Karate listed as the song, so all of the monetization from the video goes to the property owners. That said, they still probably made an agreement before uploading the video. Companies in Japan are generally hyper-focused with obeying intellectual property laws and making sure they go through proper licensing channels. Youtube allows more convenient ways to deal with that, but I have to imagine that management in UF would be a bit more on the cautious side when it comes to something they upload officially to their own channels if it involves properties of other companies.
It was shocking enough that Takahagi tweeted this unofficial upload of OG S/mileage, even though (unless it's that MM Germany guy again) the music is already claimed by UF.
It looks like more of the Japanese music industry is finally starting to "get" youtube a little bit better now.