The system should prevent 0 from being pushed as a notification. Each teacher or school should be forced to deal with 0 in some other way, preferably erring on the side of helping students, rather than punishing them.
This would actually makes teaching easier, as they can use a 0 as a placeholder without having to decide about accidentally pushing a notification.
I don’t think the teacher’s goal is to cause a panic with a transient 0 that’s later replaced — so I don’t see why they’d stop using something that better accomplished their goals.
A related issue is that many parents struggle with school website logins/passwords. I bet a significant percentage never log in, all year. But they can't ignore their phones.