The Drama Mamas recently covered the problem that arises when you want to have some alone time, but your friends keep inviting you to do things with them. It's hard to say no without feeling like you're hurting their feelings. If Real ID had an invisible mode, this wouldn't be a problem. Captain Obvious has been tapping his foot about that one ever since this feature first came out.
So all of your friends can see your real name and they can chat at you whenever they want. In Diablo III, they can even hop into your game if you don't have that function disabled. But at the same time, you can play on an alt while waiting for your friends to get online to get a group together. They can contact you easily cross-server and cross-faction -- even cross-game. The online privacy issues are huge if you aren't careful, but the convenience of chatting with friends from all over the region is also huge.
Do you have Real ID enabled? If so, do you invite people you don't know in the physical world or do you restrict it to friends who already knew your email address and real name? If you don't use it, why not?