I think it would be better if they made their own instance that worked akin to Mastodon. Then they are always in control of it and people can use whatever Fediverse account to follow
Hmmm, did they? I'm looking and I can't tell what their legit account is. There's some account @c.im that has 25k followers but it doesn't seem like the actual BBC account, just some 3rd-party not (like a dozen others).
I'm pretty sure they did, although I've used Mastadon even less than I used Twitter, so I can't be 100% sure. However I've read articles over the months saying they were introducing an instance as a trial, and then that they were keeping it running after the trial.