It doesn't need to be about "hey, come and get so and so, he's crazy". Simply the idea that it's acceptable to recognize "this isn't working very well for me, I'm really feeling off" and to seek help as openly as you would for cancer or heart disease -- and expect those around you to say, "hope you get some good news from the doc, hope you're feeling better, how's it going", rather than fearing everyone side eyeing you and whispering about you and avoiding you like you've got the plague might go a long way towards more people seeking treatment as opposed to seeking alcohol or self medicating other ways.
As far as those who do need to be held against their will because they are genuinely a threat to themselves or others, it's very surprising what happens in those cases. I've seen quite a lot of it personally. In my experience a great many people who have decompensated and have family come into court to file for them to be picked up for mental health treatment respond amazingly quickly, amazingly quickly, and it's obvious they are ready to return home. More often than not those admitted for involuntary treatment respond almost immediately to hydration, nutrition and treatment with appropriate psychotropic meds. It's not to say it's uncommon for these folks to relapse, but generally their families and friends recognize and are quicker to intervene or come back to the court if necessary.