The reason for keeping weapons such as knives out of schools (or anywhere else) is to reduce the chance of fights escalating and becoming deadly.
What has been shown to reduce the chance of "fights escalating and becoming deadly" is training in the use of knives and guns, not bans on their possession. Children and young adults who have had such training have about the same rate of "delinquency" - but the "crimes" they commit are almost never violent. (They also know what they're dealing with and what to do about it if someone DOES start misusing a knife or gun.) Kids who learn about guns and knives only from entertainment media (where blood and agony are not shown) and other kids are the ones who commit the violence.
On the other side of the world, I did not need any sign or rule to know that if I sneaked my dad's shotgun into school, I'd be facing certain suspension.
On this side of the world young adults used to bring guns to school when they were going to the range or hunting after school (or had been hunting at dawn before school) with no perceptible problems - up to the latter half of the 20th century. Interestingly, that's when the child-rearing fads started "protecting them" from information about weapons.