The cliché is girls that are socialized that way. It's still overwhelmingly true that girls will have dolls more often than boys and that it will format their behavior.
Recognising that is not perpetuating or condoning it.
Having worked in childcare / early childhood education, I've seen it a lot. Kids younger than about 5 or 6 don't care. The boys love to play dressup and the girls love the sandbox with the toy cars. As they get older some start to fall into stereotypical gender roles... and even then it's usually obvious that they're learning from / being indoctrinated by their parents. My use of the word indoctrinated is only to indicate that sometimes these gender roles are passively learned from the parents example, but in some cases there are parents that actively enforce / teach their kids to follow gender roles. For example, I've seen a father, on arriving to collect his son, react almost with horror to see the boy in a skirt playing in the mock kitchen.
Cliche is the wrong word. Gender roles in society are a topic that spans many disciplines and has a whole lot of detail to discuss. They are a huge thing, and you're right: the gender role assigned to girls does prescribe for them a lot of child rearing practice. That said, after seeing what some kids will do to a baby doll, I can confidently assert that such play is no substitute for actual instruction.
I completely agree with you, except on the younger than 5 or 6 don't care part. Maybe don't care as much, but studies suggest that gendered socialization starts occurring before 18 months. I think that this indoctrination is more common than people realize (and realizing that it's likely happened to you can be a hard pill to swallow). Especially in areas like mine, where most families are single income, it seems like the girls are always playing with dolls, strollers, ovens.
It makes me very sad.
But people will argue that it's innate until they're blue in the face, and use it as examples to 'prove' that our brains are sexed.
