Re: "Just look at Switzerland."
Switzerland is a very different type of country.
You missed one more and key differentiator between Switherland, Eastern Europe (most of which is saturated with guns and ammunition), other Western European countries and USA. A lot of them have a comparable amount of guns (and more dangerous ones too like true automatics, etc). They do not have the culture of taking a gun in their own hands and "delivering justice" on all who have wronged them.
The reason for that is simple - their culture and schools do not drill into every single person the idea that they are somehow exceptional from the earliest age. It is the American exceptionalism which is at the bottom of the USA mass shootings. The more exceptionalism is drilled into the younger generation, the more shootings you get later on. To anyone opening their mouth about citation needed - Russia. As a part of the pivot from the arising cult of personality to Vlad the Bare Chested Overlord 10 years ago they borrowed and deployed the USAisian exceptionalism doctrine. They are now literally doing the same thing USA does. So guess what - they now have school shootings too. Something they never had before when "doubting yourself and questioning how you can improve" were on the top of the agenda.