Simplistic logic that sounds nice but doesn't actually work. There are more guns than people in this country. We have significantly bigger problems with illegal drug cartels than most. Drug gangs, who have access to illicit import capability, commit the lion's share of gun violence. The right to keep in their arms is literally written into our Constitution.
Put those things together and you have a few very big problems.

The first is that any sort of gun ban will basically fail unless you amend the Constitution, which there is not political will to do by any means. And those who want to keep their gun rights will point out that there are at 4-5x as many defensive gun uses by law abiding gun owners as there are gun homicides. So it is unlikely that you will be able to get any sort of gun ban to happen.

Second, even if you did, you could never get rid of any significant number of them. There is no national registration scheme. A couple of states have their own registration schemes but those are generally not the states with the majority of firearms. Look at other countries that had similar situations like Australia, they have had numerous amnesty periods for people to turn in firearms and they still don't think they have a significant majority of them collected.

Finally the question is who you are disarming? Remember, the lions share of gun murders are committed by drug gangs. A gang that can import illegal drugs can just as easily import illegal guns. Or, guns are actually not that hard to make, significantly easier than drugs. Any decently equipped machine shop can crank out guns, and unlike a drug lab which has to be out of the country the machine shop has a legitimate day shift use so it can operate in the open and pay taxes.
Point is, you will end up disarming the law abiding citizens while the criminals will still be armed, and willing to sell those guns to other criminals.

I also very much want to end school shootings. I hate that we are turning schools into fortresses or prisons. I hate the teachers, who are already paid shit, have to think things like 'time to attack a gunman with scissors'.

But I want to spend effort and money on the policy that will most likely bring that goal about. Maximum bang for buck if you will. And I'm sorry but gun control isn't it.