Do you have a source for this? Dog attacks being more common than car accidents seems extremely unlikely to me, given how prevalent car accidents are.

I really wouldn't expect a cellphone ban for students to result in a significant rise of delayed treatment for injuries caused specifically by dog attacks. Even if dogs attacking students is such a common occurrence that it warrants consideration in this proposal (which I doubt), it's still a school. Teachers and other staff are around. Just have them call emergency services in case of injuries.