“When it is known that people in a school or a restaurant may well be armed, and that in a large group of people, the sort of group that attracts crazies intent on dying in a blaze of murderous glory, it is probable that one or more people are armed, the choice to try for mass murder is not made.”
You are assuming, of course, that a potential mass murderer is thinking rationally. Pretty big assumption.
They tend to be calculators. Places that advertise their gun-free status attract them. Places where it is known that there are armed people simply do not experience these attacks. Irrationality can and does include coldly rational elements and those planning a shooting like that are not necessarily even irrational. They have merely chosen actions that are contrary to civilization but are rational in their preparations for attaining their goals. There are occasional shooters that might not be affected by the thought that people may be armed, like Walt Whitman in the Texas Tower but in that case armed citizens or police present would not have had much quick effect. He chose his location where he would have time and it would require a sharpshooter with a rifle to end him quickly. CCW laws are not relevant to such a shooter. None of the shooters have been irrational in their procedures once they have decided what they wanted to accomplish. The possibility of encountering armed people is such an effective deterrent that one will never be able to prove it except statistically sometime in the future.