>>OTOH the number of people authorized to carry a loaded weapon for self-protection is infinitesimal ....
So there's a difference: lots of people have an assault rifle in Switzerland and know how to use it, but you're not allowed to carry it around. In fairness, you aren't allowed firearms in US schools either but still the shootups happen. So there's something else going on apart from the rules.
"... They ne'er cared for us
yet: suffer us to famish, and their store-houses
crammed with grain; make edicts for usury, to
support usurers; repeal daily any wholesome act
established against the rich, and provide more
piercing statutes daily, to chain up and restrain
the poor. If the wars eat us not up, they will; and
there's all the love they bear us."
-- Shakespeare: Coriolanus, Act 1, scene 1