To me, this whole debate goes round and round because, at the end of the day, we're just not really speaking the same language. In it's application, I don't really know if I agree that it does a lot for the public discourse in terms of allowing for people to properly self-identify by asserting that theism/atheism is a strictly binary position. I mean, we certainly can make it one. However, it strikes me as slightly disingenuous, as I don't think it properly accounts for the people who really just want to sit on the fence -- be it because of apathy or genuine indecisiveness.
Basically, I think that whole Gnostic vs. Agnostic/Theism vs. Atheism chart was seemingly created to really delve into the semantics and add better clarity to the terms. And that's great. However, in application, I don't think it really does much. If all we care about is debating semantics, then it does a great job. However, outside of futile wastes of time like this, do most people really care?
What we care about is a continuum of classification so that people can go "oh yeah, that's where I fall." And I don't know how asserting that Person A who believes that there is no God but concedes that they can't be sure and Person B who asserts that they neither know nor care about whether God exists fall in the same category really helps in that regard. Given that most people with a degree of humility on either the theist or atheist side allow for fallibility, the Gnostic vs. Agnostic division seems largely useless to me. That Persons A and B are both Agnostic Atheists really does little to distinguish where they differ.