Suffice it to say that, with near universal applicability, all human societies throughout recorded history have made clear distinctions between the boundaries of acceptable social behavior (and punishments for breaching these boundaries) for children and adults.
There's also quite a large accumulated body of modern scientific measurements which suggests that children and early teenagers lack the sufficiently streamlined cerebral pathways (pre-puberty) which would allow them to make the social judgment calls and impulse control to both avoid being a bully and/or a bullied victim. In both roles, they can not balance the short-term costs against the long-term consequences.
You also make a gross assumption about the training and responsiveness of a local police force to situations involving minors in the custody of a school. Baring extreme violence, a history of criminal behavior, or property damage, in most municipalities, this is the fiduciary responsibility of the public school district. For private institutions, a specific set of liability clauses and insurance is part of the enrollment contract.
Generally, you want to stop the bullying for one of the same reasons you want to stop rapes -- it damages the lives of many victims. But you also want to catch this, because the bully often needs help.
Edit: I don't really have an opinion on when/if the police should get involved. It probably depends on bow fscked the teacher subculture is.
You say to the thug, in no uncertain terms, "The next time you do XYZ, the consequences will be a removal from school." And, yes, have the police deal with it because they are actually equipped for such activity, unlike your typical teacher.
...and to be clear, I'm talking about instances of actual assault, and not the vast bulk of things in the category "bullying".
If making bullying a legal case is the only way left to proceed, any parent should just go ahead, and take it as far as necessary. Sometimes it's just the school administration who need a kick in their collective ass to actually do something about it. At the far end, it's the bully himself who is in need of that kick.
You are assuming that somebody wants to make things out of proportion. Is it out of proportion, for example, to call police if your kid has been beaten or robbed on the way home? You can't be seriously claiming that to protect the fragile worldview of the thugs/thieves you should sacrifice the one of the victim?