It this context, it is an advantage for men through. And maybe also for children, because a lot of what triggers "omg irresponsible" in women is actually fine.
The very same prejudice hurts men in different contexts - when good and cool things they do with children are attributed to their wifes, when they want more time with children, when they don't get chance to learn how to deal with young relatives because everyone keeps them away. When they are shamed for wanting to work with young children or presumed incompetent.
It is objectively a bad thing if men are perceived as incompetent parents, because they are men, let alone from any other stereotypes.