This is especially true in the last few games. While it is always the Master Sword that strikes the final blow, for the last few games the only way to set Ganon up to strike that blow has been with Arrows of Light. And the only way to get those arrows is directly from Zelda.In Wind Waker you don't even get the arrows, Zelda is on the battlefield shooting them. It's your job in that battle to distract Ganon so Zelda can set him up for you.
With a few exceptions, Link is always the unlikely hero. He comes from essentially nothing, he's just got the spunk, stubbornness, and reincarnating soul, that makes him keep holding on when almost everyone else just gives up.
Zelda, on the other hand, is always a big name, even when she's not a Princess (on paper) she's a mover and shaker. People have heard of her and the fact that she has some kind of power is generally known. In at least a couple of cases she's known of to at least a few people in entirely separate dimensions.