I am fully willing to admit I just remember SS wrong, but I thought it was that chasing after Zelda was meant to be the wrong thing. You discover she hasn't been taken, she's doing things that need to be done, and all Link has really accomplished in this process was slowing down her pursuers and in some cases leading them directly to her.
Here's the plot of SS:
- Link and Zelda are childhood friends. Zelda is implied to have a crush on Link.
- Zelda gets sucked down to the surface. Link decides to go down to the surface to find her.
- An old lady tells Link that Zelda went to the temple in the woods. Link goes into the woods to find her.
- Link arrives at the temple in the woods and finds out that Zelda somehow magically teleported out of there to head to another temple at the mountain. Link goes to the mountain to find her.
- Link arrives at the temple at the mountain and finds Zelda with Impa. Zelda then magically teleports out of there to head to the Temple of Time in the desert. Link goes to the desert to find her.
- Zelda enters the Gate of Time, and tells Link to find the other Gate of Time to come after her.
- Link reforges the Master Sword so he can open the other Gate of Time so he can go to the past to find Zelda.
- Link goes to the past to find Zelda, but Zelda says that she has to go to sleep to keep Demise sealed. Link goes to the present to get the Triforce to kill Demise so Zelda no longer has to keep him sealed.
- Link gets the Triforce and kills Demise, allowing Zelda to wake up. Then Ghirahim kidnaps Zelda and takes her to the past again. Link follows Ghirahim into the past to save her.
- In the end of the game, Link has decided to live with Zelda on the surface to help her protect the Triforce.
- That this is the first game in the series only drives home that the Link-Zelda reincarnation cycle is really just the continuation of a long chain of events involving Link having to save Zelda.
Literally everything you do from a broad plot perspective is directly related to going after/awakening/saving/helping Zelda in some capacity. And at literally every moment in the story, you are encouraged (by her or by Fi) to keep following her.
Not to mention that she definitely doesn't have any "agency" since her entire role in this game is to become a person who is not herself and fulfill events that were set in stone thousands of years ago.