Properly executed defensive carry does not add much volatility. Having in place defenders also results in situations being ended almost immediately which reduces the actual volatility. Most cable news shootings only last a few minutes and end the moment the asshole doing it is challenged. Once the shooting stops the situation is much easier to work through with a calm and collected demeanor as first responders secure the area and assist the wounded. As I said earlier, defending is far easier than assaulting. Making the primary response an assault team that needs to enter and clear the building adds complexity and volatility. Having multiple faculty in defensive positions waiting for the shooter to enter their zone is a much safer tactical solution. While clearing the building is still a tactical challenge, if there is no threat that presents itself it can be done in a much safer manner with each room being cleared one by one based on pre-established protocols that are already in place nationwide as part of the existing lockdown planning.

Gun control always results in a ban. The US thankfully has it built into the Constitution as the fundamental right that it is. The issue is that "reasonable" gun control is rarely reasonable and even bans aren't effective so no matter what concessions are made, when the results don't match the aspirations it progresses. The other part of this is that it doesn't generally work in most countries and correlation does not equal causation. The US is a far more heterogenous society than any of its peers and as such has an exponentially higher degree of societal tension. It is an unfortunate by product of the diversity that makes us as strong as we are. While you say that gun control works everywhere else it has been enacted, that is simply false. What actually exists is countries that have always had lower crime than the US, that at some point in the past enacted gun control and saw little to no effect. In order to support the hypothesis that it was successful, you would need to show examples of places where it was enacted and led to a reduction in crime following implementation. The only two near peer examples in a modern time frame would be the UK and Australia who both enacted draconian restrictions in the 90s. It just so happens that the 90s also coincided with a worldwide reduction in violent crime (normally attributed to the removal of lead from gasoline). Virtually every single developed country saw the exact same reduction, except for two. The UK and Australia bucked international trends during the decade and saw spikes. Immediately following the UK's strict gun control, their murder rate nearly doubled. While the US's rate was nearly 10x the UK's at the beginning of the 90s, during the next 20 years the US's was cut in half while the UK's doubled and eventually stabilized at its pre-gun control rate. Australia saw similar results while the rest of Europe saw declines similar, but not as pronounced as the US. During these years the US expanded access to guns with the number in circulation consistently rising despite the extreme reduction in violent crime and murder. Also, using fact checks alone really don't tell the full picture, they are wildly biased and when it comes to politically charged topics they go out of their way to get the result they want regardless of the truth. When it comes to guns they often straight up lie. Israel does have a lot of good lessons to be learned about effective self defense but it is nowhere near a 1:1 example. There really isn't anywhere close enough to the US to compare us to. There are plenty of schools in the US within states that allow armed teachers and so far none of them have been a target of an incident so there is no data. It's a catch 22 where they are already extremely rare and if an event doesn't occur or is prevented it doesn't count as an event so there is no data for it. Armed teachers won't do anything for gang shoot outs in the street across from frat row or people in their 30s committing suicide at 2AM on a Sunday in a parking lot of a building that used to be a school, so things like the school shooting tracker won't show any appreciable difference based on its enactment (the second scenario was literally one of the first events loaded into it when reddit started the tracker). There is plenty of actual information out there, but normal primary sources are deliberately hiding it from the masses because both the media and tech giants have a strong bias against it and are forcing the ignorance.

Dedicated armed and trained security is great to take over the police's clearing duties, but from a tactical point of view, allowing teachers to be armed is still a superior option. Being embedded and able to self protect is a far stronger advantage, even over a response time of essentially zero. Just like counter-insurgency vs guerilla tactics, not knowing which door is defended is a far better deterrent than just specifying which expected opposing force you will be encountering. Either way, addressing the causes of cable news shootings is by far the best approach versus trying to restrict a single means of accomplishing one or debating the best way to stop one that has occurred.