I am a psychologist and to be honest, I think focusing on methods is well-intended but misguided because it leaves the pain but takes away the mechanism.
I'm not convinced that even eliminating firearms completely would reduce suicide rates as much as some think because people would find another means. Even the linked piece states "nobody knows what would happen if firearm availability in the US resembled levels of other developed countries." In countries where firearms aren't as available, other methods are more prevalent. I also think there's a lot of differences between the US and other developed countries along a lot of dimensions other than firearm use.
Even if it did reduce suicides, though, what does that leave people with? It's akin to saying "we're going to take away this only out for your pain without addressing your problems."
Sure, keeping them alive long enough might allow you to intervene and reduce their pain, but the fact that they are driven to suicide to begin with suggests something failed earlier along the chain.
What we want are people who don't feel driven to suicide, not people who are unable to commit suicide.