There are further implications along these lines, too. It's isn't just ability, but willingness: at least some prospective teachers would probably be put off by the prospect of being required to be armed in the classroom.

Not that the job market for teachers isn't glutted, right now, but is "willingness to carry a gun and shoot to kill" really something that we want to select for, in teachers? It would compete with the ability to teach well in determining who actually teaches our children.