Airlines sometimes try, but the regulations are federal, and the liability for the airlines of having a "pilot with reported mental health issues" is huge as well (because ultimately it's their business on the line if things go south).

So getting pilots to self report has been very unsuccessful because of how badly it ends for them.

A couple of days ago the senate had to pass a bill to make mental health medication access easier for pilots. We will see if it helps, but it doesn't solve the root cause (punitive measures) so I doubt it'll move the needle.