Is the stratification by social class an example of correlation or causation?

This could be rephrased as: Are poor people less able?

You seem to discount that as a possibility a priori. Why? There is a plausible connection between one's ability to thrive in a knowledge or skills-based economy and one's socioeconomic status.

I don't want to discount that as a possibility, it is much more a matter of fact. A lot has to do with wealthier people being able to afford better education and generally being able to invest more time in the offsprings chances on the jobmarket. This all leads to very able people having worse chances because they had bad luck in the socioeconomic class lottery when being born, thus unnecessarily restricting mobility between social classes.