They very definitely should. Reducing access to means is a proven method of reducing suicide completion.
That hasn't been proven to any substantial degree.
We investigated changes in the proportion of firearm suicides in Western countries since the 1980s and the relation of these changes to the change in the proportion of households owning firearms. Several countries had an obvious decline in firearm ...
pmc.ncbi.nlm.nih.gov
A recent review article in Health Policy Open, entitled “How firearm legislation impacts firearm mortality internationally: A scoping review” claims that Australian and Canadian firearms legislation is associated with reductions in homicide and ...
pmc.ncbi.nlm.nih.gov
Firearm suicides in particular trend with proportion of households having firearms, but the suicide rates overall remain somewhat level.
Canada: Despite having a big reduction in proportion of households with a gun from 1989-2000. Their overall suicide rate only dropped from 13.2 to 11.7
For Australia, their households owning guns actually halved during that time period, but their suicide rate actually went up a point.
Japan has a very high suicide rate despite very little gun ownership.
Sweden's suicide rates went down quite a bit despite their gun ownership rates staying static over that time period.
That's because while people say "guns are the easiest method to do it", there are "close seconds" that are pretty much almost just as easy. (in fact, for women, they're more likely to use intentional oxygen depravation methods and intentional overdose)
But even if we pretend there's a perfect trend line, that still wouldn't be a compelling case for me.
Given that the majority of people who have suicidal ideation are a threat to themselves, but not to others, I'm not a fan of restricting everyone on the basis of what a suicidal person may use against themselves with regards to a public policy debate.
So I'll say the "harsh-sounding" part out loud.
While I'm in favor of certain gun control restrictions that would reduce the incidents of a person harming
someone else with a gun (homicides and assaults)... I'm not prepared to sacrifice any of my ability to defend myself based on what someone may due to
themselves with one.
And to be even more blunt, as someone who's a proponent of legalizing physician assisted suicide (on the basis of the notion that a free person has a right to decide whether A) they do and don't want to exist, and B) when they want to punch their ticket out on their own terms), I don't even think it's my place to try to use the force of government in the name of stopping someone from doing that.