The game definitely encourages being social when appropriate. You specifically site a variety of issues that do, indeed, discourage it. However, they exist for valid reasons. Further, they exist alongside many other elements of design that strongly encourage players to talk to each other.

The "busy" status is something players voluntarily turn on. So if they don't want people to talk to them (or send them friend requests), they have that option. If your goal is to talk to people that explicitly do not want you to talk to them, then your definition of "social" is actually harassment.

As for offline friend requests and mail to non-friends, I'm not sure how much of these decisions was low technical prioritization of development of a desired feature versus intentionally not developing it in an effort to prevent abuse like spammers sending mail to every player in existence.

There is also a free company forum feature built into the official web site. Here is yours:
http://na.finalfantasyxiv.com/lodest...4400366/forum/

Taking a glance at that might also do much to explain why said FC leader elects to have "busy" on.