This is true until you try to actually raise your kids. "Men with kids" may poll high with bosses, but the third or fourth time you need reasonable accommodations for a school pickup, you're suddenly not the type of go-getter this company values.
I would go so far as to argue that there is a single cohort "at the top of the power structure" comprised of men with no kids and men who have kids but do not actively parent. Men who have significant childcare commitments are in a lower cohort.