I have a TV. I don't know how it works. Some people say it's because of electrical waves in the air (whatever that is), others say its because there are small people in the box acting things out for me.
I don't care, and have no opinion on the subject.
Being this form of agnostic (being intellectually honest with yourself to say you don't have an informed opinion either way) is valid.
What about Santa or the Spaghetti Monster? Do we have to be (or claim to be) agnostics about everything we can't prove it doesn't exist? There's no need to prove these things because there's no good reason to believe otherwise. And no, just feeling you're right and visions don't count.
TLDR: Burden of proof is on religious people, not on atheists. Thus, agnosticism seems like an unnecessary compromise.
You claim that we operate under a strictly Boolean assumption that god either does exist or does not exist, with "I don't know" being incompatible for some reason. What is that reason? Do you have an argument supporting this claim?
On the other than, people who claim to be somehow neither atheist nor theist are being intellectually dishonest to both themselves and everyone else. You operate your life under one of these assumptions.
edit: and for reference, you can either be an agnostic atheist, gnostic atheist, agnostic theist, or gnostic theist. These cover all possibilities as the concepts are defined.