@Xanhomey, no ... only way she can be free is becoming the successor otherwise the cycle will continue until the Shinomiya Group is gone.
She is not wrong about that because she will always be a Shinomiya, even if her family leaves her alone other will not, she will always have to live with the fact she is Shinomiya Kaguya but can use that as well, by seizing control she will became master of her own fate, she will be free ... well as free one can be anyway.
As for the "patriarchy", I think people forget that in such a system everyone is a cog ... the sons are spares, they will also be forced into marriages to strengthen the family as much the women are, their "power" is a illusion, the family matters ... everyone must obey the main family, everyone must obey the head and the head must continue the cycle.