My apologies, in context it seemed like you were implying that mental health was indeed easier to get help for in the other countries listed. Which I took to mean you were saying it was indeed more of a factor and not completely irrelevant. So I assumed you didn't think guns were the main problem from that. When they are indeed the main problem.
I didn't get from your post that you were also calling for gun control, for some reason it seemed like you were against it. Sorry.
In Australia you can get like 5 free psych sessions a year or something. It’s not very well advertised, nor is it really enough to help those who actually need.
For any serious help, you’ll be looking at out of pocket expenses.