YouTube Kids was the first thing that bothered me. Google wouldn't let me allow her to install regular YouTube, so she was stuck with that horrible, insufferable crap that makes Teletubbies seem like Kieslowski. It's still beyond me why she should be barred from listening to stuff like Kraftwerk's The Robots, Bananarama's Na Na Hey Hey or Hit 'Em High from Space Jam, all of which she's much more into than whatever YouTube Kids thinks 9-year-olds are all about. Fortunately I stumbled upon a toggle in the Family Link settings that would let me let her install and use regular YouTube.
And forget about the YouTube Music family plan, that's just straight-up impossible on a sub-13 account. Then there's Spotify Kids (which is pretty much just as bad as YouTube Kids) but Spotify at least lets you lie about her age and install the regular app. (We've all heard the horror stories of Google completely shutting people out from Photos, Drive, etc. for lying about a kid's age, I'm not about to risk that just yet.)
Oh, and you're also not going to be gaming with your kid on her new phone. Google Play Games won't let sub-13s sign in with their Google account. So this PEGI-3 rated disc golf game with multiplayer but no player interaction is a total no-go.
I find it absolutely baffling how little control I have of these things as a parent. Why on earth can't I let my kid use YouTube Music? Why is she allowed to install a PEGI-3 rated multiplayer game but not play it? And why can't "sign in with my Google account" work like when she's asking permission to install an app? Seems like a pretty obvious way to go about it.
/rant