As flexible as she was, Alice had limits as well. If an order contradicted her personal beliefs, she would not obey it, even if the order had came from Anfey. Reorganizing the noble class was necessary, and she was confident in her abilities, which was why she did not care how she approached the matter.
Anfey placed her in charge of the city because he was confident in her ability, and she wasn't about to let him down. In her original plan, she only wanted to punish the heads of the noble households. However, because of the actions of some of the noble families, she decided to punish all those that decided to disobey her.
The entire province was seized by fear, but there were still noble families that sided with Alice. When she first began imprisoning the nobility, she spared the families that had ties with the military. She did not want to upset any important military officials.