It's a high cost move with questionable benefit to address the core issue (people getting killed by guns). Background checks are already a thing, yet they are executed poorly or ignored. You can't just hop online, buy a gun, and have it shipped straight to your house.
Multiple school shootings had not just warning signs, but blatant alerts that the shooter was a risk to do it long before it happened. Like a kid's own parents voiced concerned/reached out to authorities, or a kid was put in a special school because he was already talking about killing people for years prior. Yet somehow these people got their hands on a weapon.
It was already illegal, there's no point in making it more illegal. Rather than bogus laws that pointlessly restrict law abiding citizens, how about taking a look at why things that were already illegal during many steps of the process nevertheless happened uninterrupted until the point of people getting shot?
It's also not comforting that police are under no direct obligation to use their weapons/risk themselves to defend others, yet people still want to arbitrarily restrain tools for self-defense.
We do not know what solutions politicians would have attempted & what results would have happened in the absence of the 2nd amendment in that particular case, which is far from the only potential case where the 2nd amendment might be useful.