Zelda has been a little more hands on and helpful in OoT, WW, and ST. So she has been more than just the princess you rescue at the end of the game in a few of her appearances. She was actually very helpful in WW and joined in the final fight with a weapon of her own.
As a sidekick type of character she might be able to work out although I am unsure as what she could do that would make her as useful as Navi or Midna in a partner role. It would be similar to guiding Medli and Makar around in the dungeons in WW if not done well. But as an optional player character instead of Link? She would have to be someone like Sheik or Tetra to play the part of the hero. And technically neither one of them were raised or lived as a princess (at least not for very long), they had a hard life out in the world like Link.
Normally though it would be a break from storytelling tradition for the princess of the kingdom to go out on the adventure with the hero and help rescue the lands from whatever dark forces that have taken over. Slaying monsters and fighting the dark hordes along with the hero. Especially if the setting is not some type of barbarian kingdom with warrior tradition nobility ruling it. Adventuring/questing heroes do not always originate from the royal families, it does happen occasionally only it is rare. Link is almost always that everyman peasant that discovers their destiny as a hero and goes out on the adventure. That type of lifestyle would better prepare him for all the hardships of the adventuring lifestyle a over than someone raised in the royal castle. So I believe this would only work is Nintendo adds another a non traditional Zelda such as Tetra.
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