Heavy machine guns and automatic weapons are banned, as are silencers.
In most cases the buyer needs a weapon acquisition permit, issued by the cantonal police.
This will be refused if the applicant has a criminal record, an addiction or a psychiatric problem.
A special permit is needed to carry a gun in public - and is usually issued only to people who work in security, once they have passed theoretical and practical exams.
In other words, the NRA would not be interested in implementing Switzerland's approach to gun culture, even though - as you say - a lot of it makes sense.