This pair of rhetorical questions actually has a non-rhetorical answer, and it is far more interesting (though less precious) than the one implied here.
It is more correctly circular reasoning. The psychometric measure g does not break this circle at all. I will never believe in "intelligence tests" until this circular reasoning can be broken.
I do not know why the positive manifold is as it is. But it still seems like it is a precise measure of an inaccuracy.
What I am getting at in a roundabout way is that I cannot find any credible definition of intelligence that is not dependent on the these tests. If intelligence were able to measured some other way that corroborated these tests, then I will be more likely to believe them.