Looking at the nation states the Scions interacted with:
Ul'dah - monarchy, monarch attempted to abdicate and give more power to the citizens, but the monetarist class that has a huge amount of influence stopped that. Still a monarchy.
Limsa Lominsa - rule by person who wins a boat race every five years - still doing that.
Gridania - theocracy, power held by the Seedseers/Elementals. No change.
Ishgard - technically a theoracy, but I'm willing to call it a monarchy if you want. Old power system dissolved and replaced with an elected house of commons and an un-elected house of lords.
Doma - occupied territory of the Empire, Empire kicked out and monarchy restored.
Ala Mhigo: occupied territory of the Empire, Empire kicked out, old monarchy not restored. Replaced by a republic modeled off of Ishgard's new house of commons.
Eulmore - had a "mayor" that ruled unconditionally through fear and control. Was replaced by a mayor who actually was elected by the people. I'm willing to call this an "abolished monarchy".
Sharlayan - rule by a council of 100 elected forum members. No political change there.
Thavanair - changed from rule-by-dragon-monarch-in-secret to openly ruled by dragon monarch.
Garlemald - monarchy basically defunct before the scions arrive, what they're going to do next. Might be a republic like the pre-monarchy days.
And this isn't even counting the various tribes and smaller polities that the scions leave mostly alone, except to remove the "pro-primal summoning" factions from posistions of influence.
So, out of the states the scions had major interactions with, only four could he described as "abolished monarchies" - so, less than half. Hardly an epidemic... and given the fact that this is all happening around a time of major political change like an occupying empire being driven out and people being liberated, it kinda makes sense.