But the package of measures also includes "preventing access to means and methods". This is because we know it makes a difference. We have some natural experiments to show this: changing the domestic supply of gas from coal gas to natural gas caused a substantial decline in deaths: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC478945/
Changing cars to have catalytic convertors also caused a decline in deaths.
People get caught up on this. They say "merely making it harder to buy paracetamol isn't addressing the root causes, you need to do that". They're right, but they're missing the point that this is supposed to be a package of measures that also looks at why people attempt suicide.
I don't think it's a waste to look at the data and see if certain methods of suicide really stand out. It doesn't seem unreasonable to see if (this is a gross way to phrase it but here we go) easy and efficient methods of suicide are associated with more suicides. My gut instinct would say that having easy access to handguns would be associated with more suicides, as it's (relatively) more reliable than an intentional drug overdose.
Does the data here reflect that? I am not a statistician, but what's shown actually makes me question my priors. The US has a huge difference in suicide by gun rates, but the overall suicide rate isn't all that different from European countries. And, this actually surprised me, the male-to-female suicide ratio in the US isn't much different than other countries, which really makes me question my prior that "guys have handguns and thus have an easier way to commit suicide".
https://mason.gmu.edu/~atabarro/BriggsTabarrokFirearmsSuicid...
and this page from our world in data
https://ourworldindata.org/suicide#gun-prevalence
Also of interest to me is how regulating alcohol and other drug use influences suicide. Because of the failures of the war on drugs and prohibition, this doesn't seem to be a very popular topic of study, but I reckon that making alcohol harder to get would decrease the number of suicides.
Suicide motivation is usually understood as "depression", but antidepressants aren't entirely reliable in this case. It's very hard to reach inside someone's head unless they're willing to tell you. Neither of the two people I knew who killed themselves left notes. Both were on antidepressants.
The means matter.
Anyway, the focus usually reflects org structure. Solutions match org structure. If you make a Suicide Reduction Squad, they will not be able to "ensure that all children have education" to reduce suicide, they can only chase methods. After all, it's the Education Increase Squad that makes sure children have education.
There will be hard to study this theories as long as an industry is involved and politics.
I have no idea how can you use statistics from other countries and get the correct conclusions, we probably need the data from people that canceled their suicide and compare the number of gun owners and non gun owners.