Schools should have active shooter plans. Those plans (and others) are typically reviewed/filed with the local agencies.
Some agencies prefer to set up a perimeter and wait for backup (sort of the older train of thought). Some call for immediate action, but would still defer to officer's judgement on whether they need backup. Many don't have a policy, or the policy isn't immediately known by many of the officers.
Depending on the perspective and precise details, there's no way of determining the exact answer, especially on here.
Unfortunately, legally they are they just the cleanup crew, and are under no obligation to put themselves at risk to protect people in danger. Their job is just to arrest people who have committed crimes, not to stop or prevent crimes.
But if I'm a police officer outside the school, and I don't go in now, and a bunch of kids get killed, I'm going to have to live with myself for the rest of my life, knowing that I was there and didn't go in.
The theory sounds good in the planning stage but dealing with someone with an automatic weapon is likely to be a death sentence to whom ever engages the shooter.
Yes, you're right. The problem is bigger than just having access to weapons. But being able to easily buy weapons of war in an urban environment makes the situation worse.
That reason alone is why a limit on who can buy those weapons must be put in place. It can't be all weapons but there needs to be a limit on mass murder weapons. It will not necessarily stop the shootings but it will help police and such bring the situation to a stop and limit the deaths.
When call to an active situation police have several responsibilities one of them is securing the scene to make sure that no one can leave unaccounted for. They also attempt to protect those who are not already in harm's way. They need to prevent others from interfering with the situation, such as parents attempting to enter the building themselves. Then finally they must assess the best way to deal with active hostilities without recklessly risking themselves or others.
I'm confident that there will be much examination of what was done and what the police procedures were and if those procedures need to be modified based upon things learned here. The thing is those are not quick knee-jerk lessons. It's very difficult to take a dispassionate and logical view of a situation that has caused the death of others. It's even harder if someone was directly affected by this to take a dispassionate and logical view.
Ultimately that is what's needed in order to ensure that proper actions are taken next time and proper preventative measures can be put in place. So if you ask how long should they wait to intervene in an active shooter situation my answer would be as long as necessary but no longer. That time frame is highly situationally dependent.
Because if we take a hypothetical rush in immediately situation. Not only could the police be rushing into the building parents may be rushing in as well attempting to save their children. Confusion could easily ensue police could accidentally shoot parents, the active shooter may be able to abandon his weapons and blend in with the crowd of parents and escape the situation. All kinds of other scenarios that end with even worse outcomes could happen and there are very few scenarios, outside of movies, where they rush in and they get the active shooter and everybody's happy.