Whether its logged in or not then it would really be just that best that it would really be always that available because having those kind of access or availability will really be giving out that kind of ease of mind.
Well, You have written a lot just to explain that they should have contact options for everyone. No matter if the user is logged in or not. But, I am sure you never worked as support on any kind of platform before or you do not have experience managing those platforms. Usually, people contact them just to ask silly questions which they can easily know by doing a little search or by doing a little research. So, keeping it disabled decreases the workload of the support agents who write back to the users. If I have something to tell them, I should log in and report them about it.