as school administrators, I assume they have to consider the moral and practical benefits of any solution
if for example, this bullying escalated and the kid started get beat on, and there was no way to pin it on specific individuals (victim says they did it, they say they didn't and there is no witness / proof to argue otherwise), and the school administrators fear for the kid's physical safety, I can totally see them banning the bag
however, I'd sincerely hope they did a few things first, namely:
1.) went after the potential bullies as much as possible; I've said this in another thread about bullying, but I sincerely believe the greatest deterrent to bullying is getting the support of the other people, and realizing "the other people" always outnumber the bullies. This also includes the obvious requisite investigation / punishment, but as others have stated, administrative efforts to curb bullying only go so far. It's really a cultural thing and you have to get the bystanders involved in preventing it.
2.) talked to the kid's parents from the perspective of trying to help the child, not demanding he not do something he doesn't want to do
the point of "bullying getting so bad and being unable to stop it and using a practical solution" is concerning because it opens the issues of "at what point does mental / emotion bullying cross the threshold that physical bullying already crosses" and then the obvious magnitude arguments of each
it basically boils down to what the school's administrators prioritize, namely a student's right to express himself or a student's safety and well being
that's why I really really really hope this was a last resort solution after trying 1 and 2 and failing at both
if this was a case of the school administrators being lazy and using "practical solution" as a cop out, then that's just sad and they're just contributing to the self feeding loop of misery this kid is probably going go through as he grows up