Automatic log off sounds interesting to me. There are already ways to send the call to another location, including the same ACD. That might be a temporary workaround. Especially if is practically only one agent in that queue, so logging that one out really puts us into trouble.
The problem that we are more and more dealing with are groups with very little staff. Very! So very that the customer chance to meet a real person is so low that we need to think about ways to pretend there is a real person. It is a challenge.
Unfortunately, if you fire the last agent that will not make the customer more happy...