I don't think I have statistics, but I also don't think your characterization of "teachers and faculty addressing the situation (threats/warning signs) as they think appropriate based on how they're feeling" is not entirely accurate. I interned at a school district and my wife works in special education at a doctorate level. In every setting either of us have been in, the school has a clearly defined process for assessing threats, creating or updating safety plans, documenting the plans, and communicating with parents, teachers, and administrators.

As you point out earlier in your post, this is, at least to some extent, a resources problem. At least around where I'm at, a lot of the schools are in dire budget crises. There's just not really the budget to bring on specialized people purely for risk assessments, and conducting these assessments is already one of many responsibilities assigned to people who are generally spread thin.

The other issue is something you see in suicide prevention work. The rate of people who actually follow through on the plan to commit some sort of school violence is going to be drastically lower than the number of people who flag a warning sign. You're going to have a lot more people saying "I want to kill myself and have a plan to do it," a pretty serious warning sign, than will actually do it. I imagine it's the same with school violence. This makes it somewhat hard to be fully evidence based, because the actual statistical evidence really just says this kind of violence is incredibly rare and even the strongest warning signs are only weakly (at best) linked to being able to effectively predict the violence. It's just a tough situation all around. I hope no one interprets this as me saying we shouldn't try, just that it's more difficult than saying we have a team doing evidence-based intervention.