Setting the boundary of 'you can use Discord and only this channel I've setup for you and your friends' works if you've spent their whole life setting reasonable boundaries that you discuss with them. Just like an adult, reasonable boundaries are more likely to be complied with.
To the specifics, they could create a new account/server, but it's really obvious on the server list (set a unique server icon). Discord doesn't have parental controls (e.g., you can't set a settings PIN so the settings can't be changed), but there are a lot of server controls you can setup to restrict access (like really short invite times, for example).
It's honestly not something I'm worried about. I'm just saying that using the server I set up is the path of least resistance for them.
It’s super nice because they can set up channels for only some subset of the everyone on the instance, and because I admin it, I can see everything that goes on there if there’s an issue. I don’t expect issues, but the fact that I’m the admin means that a lot of her friends’ parents who are otherwise relatively strict allow their kids to use it.