You can't have it both ways, either the prospect of Anis as a ruler is seen as completely unacceptable by all sides (in which case Algard's entire stupid stunt was baseless) or Anis does have a certain amount of support she can build a powerbase off of (in which case she just has to prove she has what it takes and probably make some concessions/kiss some asses to get at least some of the magic purity faction to accept her). And let's be real, if the king and queen don't have the power to appoint their firstborn child as heir (again) the whole country is halfway lost anyway.