When I ran hosting, I never supported via Social Medai, and today, when I need help, I don't use social media.
We ran Live Chat on our servers 24/7, so there was always a way to reach out. That Live Chat was integrated with our billing (WHMCS) so as they typed, it would populate FAQ suggestions, and we could easily link to articles. Also, since it integrated with WHMCS, we could verify that the user was fully paid etc.
We used Kayako I think it was, and also LiveZilla for many many years.
Social media is good for answering a "do you support" type question, but the moment the person actually needs support, that should be taken out of the public eye and put into direct communication.
Similar with Forums. I'm all for how to type things, but if there's something specific with a particular account, that shouldn't be public information.
Today, while we offer design & SEO, we no longer provide a Live Chat type environment, and anything submitted on Facebook is quickly funneled into a ticket in our system.
At the end of the day, even if a user wants a specific thing, it's your job to funnel them into the correct support method for faster and accurate responses. 9 times out of 10, if you say "faster responses" or "accurate responses" they will have no problem moving over to the REAL support system.