You are completely right. We should not try to understand why so many more men die. In fact we shouldn't even bother recording the gender at all in the figures. What were people thinking when they started recording this pointless statistic.And as said, the reason is heavily affected by choice of method. That is not a cause to have gender specific treatments, but it could be used to restrict access to guns, to put fencing and security on bridges for example.
A local bridge near me has some good Samaritans set up in a warmed tent in the middle of the bridge over the festive season. It used to be there would 2-3 suicides, predominantly by men, each year. Now that number is essentially zero .
Programs like that can reduce gender differences in suicide outcomes, if that was your primary focus. The real solution is to treat mental health at the cause, which requires much higher investments
** This is sarcasm.