Except that Faith is also agnostic, she believes that god exists, she even thinks that she knows: but she can't know, she can only believe.
Perhaps there is some sense in which your definitions make sense. The problem with them is that people the rest of us call atheists, Christians, and agnostics definitely have different mental states that they present in reaction to the question is God real. Adopting your definitions simply means that we no longer have words to describe those mental states. No thanks.
Under a government which imprisons any unjustly, the true place for a just man is also in prison. Thoreau: Civil Disobedience (1846)
History will have to record that the greatest tragedy of this period of social transition was not the strident clamor of the bad people, but the appalling silence of the good people. Martin Luther King
If there are no stupid questions, then what kind of questions do stupid people ask? Do they get smart just in time to ask questions? Scott Adams