I think it contributes to a renewed sense of purpose and dedication that comes from knowing you are responsible for other people and a desire to show them a positive role model.
I'd be confident the extra leverage on parents is a larger factor.
Increased leverage to me would imply suppressed wages.
edit:
I also think employers will often empathize with new parents who may be operating on reduced sleep and hours, giving them a little more leeway than otherwise. I know I do this with my employees.