@elftummy @Yurt_Dweller correct me if i'm wrong, but for the majority of ocarina and wind waker you aren't trying to save the princess either. the focus is on saving hyrule and zelda is around and kicking in some form or another for the majority of the game.
idk about twilight princess because i never really played it past the intro.
skyward sword is about finding the princess but not necessarily saving her. she's with impa the whole time and you just don't really know. originally, you would actually play as zelda in skyward sword but they ended up cutting it and just turning those segments into the relevant cutscenes instead.
breath of the wild is a bit closer to saving the princess, but it isn't like ganon has her locked away somewhere and you have to defeat him, it's that she's battling him and has been for 100 years and probably could go longer, but hyrule itself will never be saved if link doesn't step in and give zelda aid.
@elftummy @Yurt_Dweller i honestly kind of see majora's mask as a 3D link's awakening, because you're saving this whole place from being destroyed by a strange entity and it may or may not have actually happened.