>If "will power" was a strongly inherited trait, and the theory is that will power leads to increase household income in adult life, then this controlling would remove most of the signal.

If some underlying willpower was the cause for the behaviour and willpower would lead to better outcomes, then there would be differentation between children within the same income bracket who score different on this test, right? But that is not the case:

This new paper found that among kids whose mothers had a college degree, those who waited for a second marshmallow did no better in the long run—in terms of standardized test scores and mothers’ reports of their children’s behavior—than those who dug right in.