Yes, little demand by criminals because there is low gun ownership with the lawful. Lots of lawful ownership guarantees lots of criminal ownership.
You have zero proof of either of your statements. You are assuming a causal link where there is none in both cases.
Every male Swiss citizen keeps an ACTUAL battle rifle in his house if he is part of the militia. how does that translate to Swiss criminal gun ownership?
The Truth About Guns in Switzerland - The Coalition to Stop Gun Violence
In Switzerland, all able-bodied men between the ages of 18 and 30 are conscripted for three months and issued either an assault rifle or a 9mm pistol (the automatic or rapid-fire function is removed from these firearms so they fire only in semiautomatic mode)
after completing basic military training. These firearms are kept in the home and are to be used only for military purposes, not for sports shooting or personal defense. After initial training, members of the militia are required to do three or four weeks of military service a year until they have served a total of 260 days or reached age 34. Additionally, a law enacted in 2008 requires all army ammunition issued to militia members to be stored in a central arsenal. This citizen €™s militia complements a small number of full-time military personnel to constitute Switzerland €™s army.
Many Swiss men buy their service firearms after they finish military service. Since January 2010, however, they are required to obtain a permit to do so, and must provide some justification for keeping the gun.
[Editor €™s note: Swiss women may volunteer to serve in the armed forces and can now join all units, including combat troops.
Currently 1,050 women are active-duty members of the Swiss military.]
Laws governing the private ownership of firearms are equally strict. In 1999, a federal law on arms, arms accessories, and ammunition (the Arms Act) came into effect. The Arms Act requires a permit for each transaction involving firearms or relevant parts of firearms purchased from an authorized dealer’s shop. Permits for purchasing firearms are issued by the cantons. Buyers are carefully screened and have to meet a number of requirements (i.e., minimum 18 years of age, absence of any apparent risk to the buyer or third persons, no entry in the Register of Convictions for violent crimes and/or misdemeanors, etc.). Subsequent transfers of firearms among private individuals have to be documented through a written contract, which must be kept for at least ten years. Additionally, several cantons require citizens to register firearms.
Any person wishing to carry a gun in public must obtain a separate, special permit from their canton. The screening process is essentially the same as for the purchase of firearms. In addition, applicants must demonstrate a legitimate need to protect themselves, other persons, or goods against specificrisks. Applicants must further pass two tests, one on the correct handling of firearms and one on legislation concerning the use of firearms. Permits are valid for five years. Certain exceptions to these rules are made for hunters, those performing military service, and those participating in shooting events.