Depends on the players I guess. Civ players seem to dread nothing more than a dynamic evolution of the political map and a game in which you lose territory or cities. People that play Europa Universalis should be more used to losing things – even though independent colonies have become very rare in that game. But people that play the Crusader Kings franchise should be very accustomed to losing all kinds of things a few times during the game: territory, troops, power, titles, skills, abilities. The up and down (and preparing against the down being too bad) is generally seen as a big part of the fun in that game.
I think if there is a way to interact with a potential independence beforehand – e.g., events in which you can choose between more yields in DL vs. giving them more autonomy (= less yields for you) or sending gold and/or troops to appease, declaring a city a DL-specific capital – this would give you a choice: try to keep the DL integrated but for a price or fight them to reintegrate them after they declared independence. Hopefully, this would also not feel too scripted if done well, as potential triggers/weights could depend on a myriad of factors: population in DL vs. homeland, amount of treasure fleet points in previous age, troops built in DL, DL culture or gold output, number of resources, number of cities vs. towns in DL, distance between HL and DL...
