So you're saying that Zelda knew from the day that she able to comprehend the world, that she was destined to run away from evil and possibly be kidnapped by it while waiting for some crazy kid in green to show up and save her?
I'm going to assume this is a joke response mostly... if it's not then I'd have to question the point of this. Nevertheless you're really spinning and stretching my words.
Regardless, to add to that... she wasn't even really running from evil in The Wind Waker even though she was being searched for and didn't in Ocarina of Time until near the end of the first arc of the story (remember she also tried to stop Ganondorf, although that didn't work out due to a certain unexpected occurance).
Zelda may be a princess- and therefore privilaged, but that doesn't mean she can't be capable. Padme Amidala could kick butt, for instance. And the amount of wealth and influence Zelda has should be able to get her access to more weaponry and magic- like how Bruce Wayne had the money to become Batman.
I'm not necessarily saying that I'd like to see a game entirely revolving around Zelda, but it'd at least be nice if she had as much screen time and chances to fight or otherwise show her abilities as Link.
Other people already answered this already so I'll sum it up simply...
Ocarina of Time she used her knowledge and visions to try to guide Link to find the stones and as Shiek assisted Link while evading Ganondorf. Near the end she also used her spells to unseal doors and seal away Ganon.
A Link to the Past she helped provide advice to Link throughout the adventure despite the fact that she got captured (see, even when captured she still has her uses).
The Wind Waker she helped Link get into the Forbidden Fortress and save him from Ganondorf when Link first walked up to him with the Master Sword. She also helped Link out in the final battle. I mean... that's basically what you're asking for right? For her to take some action and fight? She basically helped out in the battle against the last boss and saved Link once.
Even in The Minish Cap, which is one thing no one seemed to have mentioned yet, she was the only one who tried to contest against Vaati's power at the beginning with her magic. Just that Vaati happened to be more powerful than her and thus turned her into stone.
Amidala? She really didn't have as much action time, nor were her action sequences as influential outside of self preservation moments, as Tetra/Zelda was in The Wind Waker (did she really help out in the battle against the Sith? Perhaps as a politician to some degree although it was more like being manipulated by Palpatine in early parts). She also provided less advice than Zelda did in A Link to the Past and Ocarina of Time, so there goes any wisdom argument as well.
She does what she's capable of doing given what powers she has. She has magic in some games, but that doesn't mean she should go headstrong into things especially when the enemy apparently has even stronger magic.
Considering she has the Triforce of Wisdom I think it's not a bad thing that she basically played the role of a guide in Ocarina of Time as well.
Also, to target one of your older quotes... she basically did run the entire show in Ocarina of Time. She helped fill in the rest of the story about the Triforce to Link (that began with the Deku Tree) and sent him on the mission to find the three spiritual stones, then helped to guide him again as Shiek.
She plays her role well enough. The thread seems to make her out to be useless but the fact is she plays a huge role in most of the games (and some may very well argue that her role in Ocarina of Time, while consisting of less "action," fit her role better as the possessor of the Triforce of Wisdom). I don't even see it to be too big of a deal that she's physically less capable than Link, as long as she plays a direct role in the story and provides help for the hero all will be well.
We'll always play as Link, that's our "link" into the game for us to be the hero. Zelda will always be a catalyst and she will continue her role as one of the major characters that guide the story, playing her part whatever it may be. She'll never get as much screen time as Link simply because... we're not supposed to be her. Plus the whole thing about her handling things on her own has already been argued against in the first page, if she is so physically capable why does the player even need to do anything? And please... don't respond saying that we will play as Zelda as that's kind of destroying the point of Link...
I also feel that it is mostly her story in the recent main games. Link has a few personal side stories in Ocarina of Time and The Wind Waker, but that takes a backseat to the bigger scope of things. It's really hard to argue that Ocarina of Time isn't her story seeing as she's the princess that is constantly mentioned during the second arc of the story, she guided Link both young and old, and it's her kingdom and her castle that was overrun. The only thing missing is seeing the world through her point of view, which really isn't right for a Zelda game anyway.
The Wind Waker... really wasn't anyone's story really but rather a story about the Kingdom of Hyrule itself. Zelda was still a catalyst in everything in the end. Outside of arguably Link's Awakening and Majora's Mask, both side stories, the games never did have the world revolve around Link.
A character can still be a central even if he/she doesn't vanquish the evil in the end, as long as her part in the story is very important. Take a look at Sleeping Beauty for example, she's obviously the central character in the story but it was ultimately the prince who came and vanquished Malificent (with the help of the fairies) and saved the day.
Really, the original poster's arguments were kind of debunked in the first page