The first principal component of scores on various tests is, of course, a mathematical artifact. But it's not the real thing, it's just an estimate, a finger pointing at the real thing.
I agree that people can be both stupid and smart in very different ways, but at a certain -- and useful! -- level of aggregation, there are generally smart people and generally stupid people. There is a lot of variation around that axis, but I think the axis exists. I'm not arguing that everything should be projected into that one-dimensional space and reduced to a scalar.
Here is how this game works. We have a bunch of observed variables X, and a smaller set of hidden variables Z.
We assume a particular model for the joint distribution p(X,Z). We then think about various facts about this distribution (for example eigenvalues of the covariance matrix). We then try to conclude a causal factor from these facts. This is where the error is. You can't conclude causality that way.