I think the entire reason Navi has an annoying quality is mostly just from the perspective of veterans of the game. Personally, I thought Navi was an immensely helpful addition to the game the first time I went through, but then I did again and again, and there's a certain breaking point where you're going through your fifth time or so and you still haven't quite got it to where you can do the timed quests to get the Biggoron's Sword on the first try so you're getting all stressed out, and then Navi keeps saying, "Hey, Listen!" and you keep swearing and shouting "NAVI, SHUT UP, I'LL GO TO THE FOREST LATER!!"
After a while, I guess I didn't mind her as much anymore because I can now go through the game with pretty much all the side quests in just a lazy Saturday afternoon. Including the stupid timed quests which were an immense pain in the *** the first several time you did them, and things such as the Ice Cavern, which are annoying every time you play through the game.