You make a lot of generalizations here. Do you really believe it is this way for all, or even the majority of, quiverful daughters? I have no doubt it’s happened to some, and I support you in standing for those women and girls. But it is not this way for all, yes they learn to cook and they believe their place is at home, but most have plenty of friends, plenty of free time, and are taught how to have an opinion, because they need a strong opinion against the common opinions of the world. And I don’t know a single QF family that dosen’t value an education, many a quiverful mother has spent their time worrying about whether their children, sons AND daughters, are being educated to an appropriate level. I’ve never, in modern day life, heard it called dangerous for girls to be educated. Even in the arts of homemaking, an education is valuable and vital, and a woman can have dreams outside the home without usurping her husbands headship. I have big dreams, and they are both within my home, and outside of it. I don’t dream of becoming a company CEO sure, but I dream of influencing peoples lives. Which is grander?
Girls who are in the situation you describe should, most certainly, be spoken for. But please don’t label every daughter of a patriarchal family as living this life. Maybe 20 years ago it was different, but, at least from my view today, very few families live the way you describe. What you describe is more true of Islam than christian patriarchy.