The last known living member of the Royal Family is Wildergelt in the MNK quests who interestingly didn't realise he was and was horrified to find out. Without spoiling those quests its fair to say he has no interest in pursuing a claim.

One of the give things we will see being dealt with in the patches is what Ala Mhigo does now. The resistance we have been working with is only one of the resistance factions and even then there isn't one single unified opinion on what form of Governance Ala Mhigo should have. That is one of the reasons Conrad picked Lyse. She has traits that almost everyone involved will at least somewhat associate with, if only just being the daughter of a hero of the people. Further, she wants an Ala Mhigo which is inclusive of everyone, even people like Fordola who operated under imperial rule.

Compared to Doma, that has a clear transition of power, Ala Mhigo is a much more difficult case and likely we are going to have to way in a lot to keep things moving smoothly.