But I still think that the American idea that they make ordinary people safer is simply plain wrong, there is just too much evidence to the contrary.
Is there? In my own country gun control was imposed over a decade ago... the statistical analysis since then have largely concluded that the ban had a statistically insignificant effect on the crime rate, with a minority(largely organized by pro-gun organizations) asserting a statistically significant increase in crime.
Notably their haven't been any studies, even those organized by gun control advocates, that asserted a statistically significant decrease in crime... I emphasize, those studies with a bias in favour of finding that gun control reduced crime weren't able to justify that assertion. Which is remarkable considering how easy it normally is to find some statistical evidence, no matter how shallow, that "proves" your point.
