It is not a right of the militia, it is a right of the people. I, for one, am part of the people. Are you?
The right of the people to a militia. Which you and I both have, in our state's respective National Guards. Really the biggest threat to this right is the federal government using National Guard for foreign operations, as has frequently happened in the war in the Middle East over the last 15 years.
As far as teachers being armed, is your only defense against it is that we have some kink of lack of workers?
I'll parse out the flaws a bit more. Ignoring the fact it would increase gun violence, which I'm sure you'll dispute, we'll just focus on the pure policy flaws with it.
It will massively increase the cost of teachers. Like, to a factor of three or four times their current cost, at a minimum. Almost no current teacher would be qualified for this, and I can't imagine many would even pass the training to a satisfactory level. We are currently under-funding education. You're massively increasing the cost of education, which isn't politically possible.
To be flippant, we won't even give teacher's enough pencils and notebooks, and you think we can add the cost of weapons, additional insurance, training, and the massive pay increase to every teacher?
There's also no precedent of this working. Our closest case-study I can find would be the massive increase in school resource officers (Armed, trained police) in schools post-columbine. I can't find an instance of a school shooting stopped by these officers. I can literally tell you more times that a school resource officer has lost their gun than stopped a shooter.