I am not in the slightest 'vastly over exaggerating' the problem, at all - I've seen several people succumb to cancer & absolutely all of them had horrible mental health problems, the issue is I think you're just thinking of 'general mental health issues' - and the absolute vast majority of these situations are people with other life ending illnesses that are having trouble facing their mortality which creates extreme mental health reactions - I have first hand experience in it unfortunately in witnessing this happen.
It's alarming how no one at all recognises the serious mental challenges that literally change a person when they get cancer - they either fold, get extreme depression and anxiety or go problematic, violent, angry at anything and everything, bitter hateful to the extremes (which is a problem for many older, particularly white males who are in ok health, let alone cancer sufferers)
50% of people get cancer, its a problem you cannot skirt forever - and in relating to the OP, guns - im glad the UK has relevantly good gun laws, it would be a lot worse if not.