Anne-Sophia doesn't want the throne for a variety of reasons. She doesn't want to marry a guy, she doesn't want to hand the secrets of magicology over to a husband, she doesn't want to lose her freedom, she's utterly terrified of the sort of ruler she could become... etc. Many many things.
The bset option seems to be for Anise and Euphie to become co-rulers. Anne-Sophia will be queen, with Euphie as her consort. The queen will make the big decisions and whatnot, and Euphie will support her and handle the day-to-day stuff the way she's been trained to do for most of her life. That will also help ensure that Anne-Sophia still has free time to pursue her research: another concern she has about ruling.