https://time.com/6218385/suicide-rate-new-mexico/
White men in particular are checking out at an alarming rate.
So while this is an "external" cause not counted in the stats of the article, I can't help but assume common causes. The kind of depression that makes you want to die also makes you not want to take care of yourself.
It isn't difficult to get state paid medical care here, except for the distance. Appointments at the two small clinics are not far in the future and the medical staff is competent. I doubt doubling or tripling spending there would have much if any effect.
I think it's more about people who have chosen to live a more traditional lifestyle and discovering that it's an increasingly poor fit for the modern world. A plague of psychiatrists could descend on our county like locusts and bury every depressed person in talk therapy, and I doubt it would help.