Cassandra and Claire were really impressed by the plan of Merchant. On the first floor, blood is given the highest regard when it comes to giving someone a title like the head of the family. For example, a woman or a man from the Cross family when married into the Cullen family then she/he could become head of the Cullen family if they hold enough influence.
If all the important family members die then Phyllis and Cassandra actually would be entitled to major roles in the family. Cassandra was the daughter of a concubine of the second master of the Cullen family. While Phyllis was the product of old master r*ping a woman when he was drunk. Because of these things Cassandra and Phyllis were not regarded as the main family. They both may share the blood of the Cullen family, but they were a product of the lust of the Cullen family men.