There's a massive difference between uninstalling mods and beginning a new game in 100% vanilla with no mods ever applied.
When the game is saved with a mod running, the reference data from that mod will remain in the save state and cannot be removed. (This is true of all games once they're modded.) That reference data is not guaranteed to cause any issues, but it certainly can and will depending on which mod library was used.
One of the most problematic things a player can do is save the game with mods loaded, then remove the mods, and load that same game. That's where the big problems can come from, as the save state may now contain reference data to files that no longer exist since the mods have been removed. All sorts of weirdness comes from that, from broken quests, to mechanics not functioning correctly, to outright crashes or the game refusing to load.