How not? You mean to tell me that the people in province X are going to turn down an opportunity for self-rule because a nation that once occupied that territory happened to be a different culture, or that there is absolutely no one of that culture left in that province?
Umm, heck yes. This isn't the 19th century, people care much, much more about being able to be well defended and the respect of their ancient rights. It was not uncommon for the populace to want more direct control by the monarch and less from the vassals - even for monarchs of a different culture. The best example would be the Ottomans. You have a number of ex-crusader states ruled by Frankish/etc. nobles. Athens is not going to spurn the safety and orthodox supremacy within the Ottoman Empire just to be governed by some Florentine nobles because they used to own the place. By 1600 (when the DoA cores should historically expire) the Greeks of Athens have enjoyed decent relations with the Turks and lots of peace. Creating a Florentine state would mean all sorts of difficulties with the Pope and also would require adopting the laws so that the advances under the Ottomans would be respected.
Likewise, Karelia isn't going to be too keen on reviving the overlordship of Novgorod. Their lands were basically fleeced by the Republic and withdrawing the direct protection of the Tsar invited Swedish aggression.
The important thing to remember is that while cultural rebellions were a thing by the late game; early game the peasants would generally advocate for whatever arrangement made it least likely that they would be invaded and heavily taxed. Sometimes that meant seeking independence from major states; sometimes, however that meant asking for direct rule from the monarch to cut out the local nobility.
