We have this kind of system in my profession of Medicine. On a state wide basis such formal networks exist, staffed by such Samaritans that you mentioned. They are peers who volunteer for this on a part time basis. Anonymity and discretion are guaranteed. Unfortunately such networks cost money to administer and I am doubtful that any entity in Aviation (FAA, airlines, unions) would be eager to pay for it.
I mentioned earlier on in this thread that a 'Supervision' model as is practiced for example in the medical field is long overdue in aviation. We have had plenty of very hard lessons and learned from many of them, but not all. While technology and maintenance have vastly improved, we still believe that the humans at the controls should perform flawlessy day in and out without giving them much attention beyond checking their technical skills at regular intervals. This is not enough. We must also create good working environments, work patterns and a system that addresses the psychological needs of people.
Regarding the added costs, an old aviation adage springs to mind:"If you think safety is expensive, try an accident"