To anyone talking about Anis Trying to implement a republic:
This is cut from the anime and likely will be cut from the manga as the manga is told from Euphie's perspective, but Anis' removal from the line of succession had nothing to do with her demanding it. She was allowed to set up a city parliament in place of the appointment of a district lord when the previous titleholder died. It failed its duties within a year because of the lack of general education. The reason she was allowed to attempt that is because none of the nobility want to handle the work and neither Orphanse or Sylphine can afford to manage the city either. Setting up a system that can run itself with the occasional glanceover from the King, Queen, or Grantz to make sure theres no serious embezzeling or legalized murder sounded like a good idea.
Edit: the books are austensibly historic records written by Lumi 1000 years later, and include biographical perspectives from Anis, Euphie, and Al. The manga is specifically written from Euphie's perspective, where as the anime is from Anis'.