Any school shooting recieves coverage often on a national level, permanent memorials, etc While far more students die on a regular basis of other causes like car accidents and no memorial or permanent reminder nor news coverage beyond the immediate area.
This gives a perception that it is a bigger issue than it is as you will be bombarded and reminded of any shooting.
Many school shootings, but not all, have allowed the shooter extensive time to act. This has often included finishing off or shooting previously wounded victims, or searching for victims and giving close range shots.
Bullet resistant material is primarily useful when it is accompanied by return fire. Like with police or soldiers who are armed and begin shooting back. When not accompanied by return fire the attacker has more time for precision aim, less pressure, and can continue to deliver rounds until they get the result they want.
When accompanied by return fire ballistic protection reduces the effective hit zone while putting pressure on the shooter. When not accompanied by return fire a reduced hit zone is less helpful, and the shooter has the luxury of aiming or shooting without pressure to get the result they desire.
It theoretically could help while briefly exposed while making a run for it, but the increased weight of the resistant material on a child is likely to slow thier running speed and as a result increase how long they are exposed to gunfire.
They may also still be injured or downed by the level or protection provided by most casual bullet resistant material so vulnerable to subsequent shots.
Negating the benefit.
Also keep in mind a few things.
As a result of security changes in many schools students do not have access to thier backpacks while in the classroom, where they spend most of thier day and have the highest percentage chance of being when a shooting happens.
A bullet proof backpack in the locker at the time has no impact.
They are unlikely to have rifle plates or ballistic protection equal to even most handguns rounds without being seriously encumbered by the weight and heat of the garment. Being less than that worn by police officers if the fabric can bend and move without looking like a ballistic vest.
Meaning it would be unlikely to even stop the rounds of weapons often used while still encumbering the child.
Most police vests are stiff and uncomfortable and still not that useful against most rifle calibers, a child would likely be wearing less protection.
While when loaded with books they already have a level of protection similar to what purpose made material would have. (Consider phone book bullet tests you often see, and consider hard cover books are even denser.)
The result is a kid would not likely have the backpack, probably never need a jacket, and be overheated and uncomfortable long term trying to wear something that quite likely wouldn't even provide a lot of help if they did experience a shooting.
On top of that they are expensive, and children often lose or misplace jackets and backpacks or have them stolen. Adding a costly expense that may be more than a one time deal.
They also wear out if exposed to liquids, sweat, etc and would probably need to be replaced a few times throughout K-12 or beyond.
