The Swiss also have compulsory military service for every man over 18 (women may volunteer), so the people owning these guns actually know how to handle them safely and have been trained to have some self-discipline.
I expect that the 18 week bootcamp affords an opportunity to closely observe all such conscripts and screen them for mental health disorders and behavioral problems, and that the (minimum) of 7 years of reserve service allows ongoing monitoring.
Additionally, common sense tells me that Switzerland's equivalent of "dishonorable" or "other-than-honorable" discharge would result in that person not having the opportunity to buy their service rifle, and possibly putting up roadblocks to owning a gun at all.
Therefore the people in Switzerland most likely to cause gun crime do not have ready access to them. That is quite different to how we think about it in the US.
If you were to seriously propose such a system in the US, I think you would get far more opposition from the pro-gun groups than the anti-gun groups. In fact, anti-gun groups would welcome adopting the Swiss system, since it so closes matches the legislation they have tried to enact such as magazine size restrictions in California, "red flag" laws in other states, and mandatory trigger locks. All of those laws have been opposed by groups like the NRA.