Quote from http://forum.square-enix.com/ffxiv/threads/73680:
"From several users on some of our more congested Worlds, we have received requests for a feature which automatically logs out characters who are AFK for an extended period of time. We are actively looking into the implementation of such a feature, but have decided to first concentrate our efforts on increasing the number of Worlds and optimizing the Duty Finder servers."

Analogy: Adding cars to a popular rollercoaster ride won't solve the problem that people are sleeping on it and preventing other people from enjoying the ride. Also, it might result in further instability with the ride itself.

I don't care if the servers have to be down for a bit for them to implement this obvious fix, they need to take care of it now.