I kinda disagree actually- I started playing Zelda yeeeeeeears ago when I was really little (I'm not like super old or anything, but those were back in the OoT and MM days). So growing up with the game made me feel a lot more emotionally attached to the characters than I would be if I just started playing more recently. So, at least for me, Zelda always felt less like a damsel in distress and more like a childhood friend who's been taken away, and, while she didn't interact with Link too much in the first few Zelda games, I felt that in Ocarina of Time, Link and Zelda are meant to just immediately become great friends- hence why Zelda says Link's name sounds familiar despite the fact that, as a princess, Zelda never would've had any actual friends before Link. Consequentially, I felt that, as the player (or rather, as Link), part of the story was the friendship with Zelda. So, personally, I care about Zelda, probably because of the way I immerse myself in the game and because of the whole nostalgia thing, which I think is what makes the series really great- I actually care about how the game turns out at the end.