Before I go further, I'm not disputing your argument about guns. I think you're making a reasonable point.
Your claim that "Our mental health is no worse than that of any country" is mostly false. We have higher rates of mental health issues than all other high income countries.
20% Can, Swe
16% Nor
11% UK
9% Ger
4% Fra
That's just reported issues. You can assume that more than 1 in 4 US adults are dealing with or have dealt with mental health issues. It's a problem.