> Is that a valid thing to do? 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.

I suspect you might misunderstand what "controling for" means.

Suppose you want to predict A (here "increase household income in adult life") using variable X (here "will power"). You do this by regressing A against X. Saying that you "control for Y" (here "income of a child's household") just means that you regress A against both X and Y simultaneously.

What sense does that make? Suppose that you regress A against X and conclude that "X explains some of A" (these are vague terms which I can make more precise if you want) and you hope that your correlation is capturing some narrative of causality. Well, someone could come along and say "yes, A and X are correlated, but actually the causality is Y causes A, and X just happens to be correlated with Y. So you're focusing your study on X when the interesting dynamics is on Y". This is valid criticism.

One way to mitigate that criticism is that you study how A depends on X while controling for Y (i.e. you include both in the regression). The rationale here is that if the result is that "both X and Y explain some of A" and someone makes that previous criticism you can respond "Yes, you're right that Y has some effect on A, but in addition X also has some effect on A, independently of Y. Therefore, X has signal regardless of whatever is going on in the dynamics between A and Y."

So, to answer your question: Yes, it's perfectly valid if you mean "controlling" in the sense that it is used in statistics.