It would be somewhat difficult to use power-control theory to explain an overall drop in crime because power-control theory has more to do with the relative likelihood that young men and young women will commit crimes. Power-control theory holds that young men in patriarchal families will be much more likely than their sisters to commit crimes. By contrast, in more egalitarian families, there should be more equal rates of crime for boys and girls.
If a power-control theorist were forced to speculate about declining crime rates in the US, they would probably say that it comes about as a result of increasingly egalitarian family structures. In such families, the fathers presumably pay more attention to their children and boys are therefore more controlled than they would be in a more traditional patriarchal family where the father works and the mother cares for the family. They would say that boys have been made to be more risk averse by the closer supervision from their fathers (and perhaps from mothers who have greater authority because they are more likely to hold positions of power in the workplace and at home).