Schools already heavily discourage Discord use, but most students use it. Most students aren't bullied, either, so the bullied students complying only further isolates them. It's pretty intrinsically anonymous, too. Accounts need to have a phone number on record, so in theory one could subpoena it... but it's not like a correct phone number is needed for everyday interaction.
Also, sometimes the bullied student isn't even in the message chain. Taking pictures of students at school, then manipulating them and circulating them online and getting everyone else at school to laugh at the victim student when they return is a common tactic.
Then you have Student ABC complaining. Students have been counseled to stop but it keeps happening. ABC believes student DEF did it, and some corroboration that it is student DEF such that the school is now 90% sure that student DEF is behind this. Student ABC is the subject of increasing ridicule and is now doing poorly at school. What's the next step?