Studies have shown suicide rates are higher for soldiers possibly/ most likely because the types of people who join the military are also the types of people far more likely to commit suicide even if they were not soldiers.

The danger of causation vs correlation. I agree, its something that needs to be factored in. Thankfully it had been factored in the studies I've read. Based on those studies, active/deployed military has a higher suicide rate than reserves/undeployed. Both categories have a higher suicide rate than the civilian population. That would imply that both factors are at play, those more likely to commit suicide join the army at a higher rate, and active duty also impacts suicide rates.

My point is there is evidence that the military has a suicide issue beyond the regular population, and providing mental health and support services to all military members, reserves, undeployed, deployed (all those people are also considered veterans btw).