I mean, if we extend your logic, we should monitor everyone at all times because someone might just accidentally do something to hurt your child right? You never know why an extremely rare event like you mentioned could happen.
Edit: also, cameras don't have to be secret. Knowledge that they're being recorded can often stop it happening the first time.
(I realize this isn't really addressing your intended meaning, but the ambiguity is there in what you said, which is pretty...)