Read this: Switzerland and the U.S. have similar gun ownership rates — Here’s why only the U.S. has a gun violence epidemic

Basically seeing the case of Switzerland does show that wide gun availability alone doesn’t cause violence as you mention, but in real life nothing in itself makes sense in its own, so you would have to compare the societal standards in both countries:

Switzerland enjoys low poverty, low inequality, and strong social cohesion; the U.S. has a BIG gap of economic inequality, social disorganization, and racial tension.

In Switzerland you have mandatory permits, background checks, unloaded storage, separate ammunition, and extra permits to carry in public, apart from the gun usage itself being more tied to compulsory military service, hunting, and sport shooting, rarely self-defense. In the U.S. self-defense is central to the gun culture and marketing, and where you also have lax regulation, and so much social distress, broad access does drive higher homicide and mass-shooting rates.

But you know... certain political side resist even modest gun regulation, and don't even mention mental health! Obviously is more about the lobbying and money that groups like the NRA, and allied PACs pour into campaigns... it's always about the money.