I'm not specifically talking about Thordan VII. Ishgard's ruling class are noble houses. Thordan VII also comes from a noble house. Aymeric was adopted into a noble house. Throughout the whole expansion it's the church, nobles and the knights who are causing us trouble. The Ishgardian theocracy is powered by the church and the noble houses whose existences are intertwined. I didn't think that needed explanation.
As for Ala Mhigo, why would a bunch of average, pissed-off citizens who just took back their own country without the help of the nobles who destroyed it and paved the way for Garlean takeover decide that they suddenly need to find a random jerk who crawled out of a specific womb just so they can rule? It could have been different if the monk NPC did the Estinien thing and came out of the side quests and into the MSQ to lead the army to victory but that's not what happened and he wants nothing to do with nobility or his family's "birthright".
Not sure what you would have expected for Eulmore. Would it really have changed everything for you if some random captain of the guard said "I'm king now, I guess" and the story never talked about it again after we move back to the Source?
And again for Garlemald. From at least ARR they were described as a former republic who started doing bad things as soon as they became an Empire so I'm not sure how someone could imagine them staying that way when none of the named ruling family exists anymore. They had 2 civil wars in the span of a year because they couldn't decide which royal butt deserves to kiss the throne when meanwhile they had 600 years of stability as a republic.
Edit: I could imagine the Ala Mhigans wanting to revive their monarchy if they had a favorable opinion of it. That happened with Doma. But the Ala Mhigan monarchy in recent memory purged their own noble houses and destroyed their own culture and religion before falling to a civil war that weakened the nation enough to be taken over with relative ease by Garlemald. As far as everyone knows, there's no one even left who could sit the throne. But the monk NPC (whose name I'm too lazy to look up right now) doesn't want anything to do with that history and has always been a monk. If he took the throne, old resentments that have since been buried would come back up. There's still Ala Mhigan royal loyalists calling themselves the Corpse Brigade in Thanalan and they're not exactly the friendliest people.