Link is not lonely. People look at him as their savior and in the same breath they think: poor hero, saving the world is such a lonely, tediously painful job.
But for Link this is not so. He has always been alone. He is an island, and his silence speaks for him. But Link is not lonely.
Link likes saving the world, believe it or not. He likes fighting monsters, blighting them out of existence so that the world is a lighter place, even if he is the darker for it. He likes the strain he feels when he moves in a new way, uses a weapon differently, finds a new combination. There are endless combinations, and Link loves to master them. It is order for him.
Order for other people is a warm bed to go to, a fire to sit by, a family to joke and chatter with. Link has never had that, not really. Growing up, all he ever had was Saria, and he doesn't even have her now. But even Saria couldn't keep his eyes from wandering to the stars, the tunnels, the treelines, and just about any direction they conceivably could. Maybe that is why…maybe that is why she knew, and said she'd always known, that he would leave someday.
Other people are comfortable with their warm beds and houses, but Link thinks this must be because they have never known the feel of the cold earth on their back through a tunic, a tuft of mist escaping the lips as the stars shine overhead, and Epona's warm muzzle on their hair. It is cold, and it is damp, and there's a fair chance he'll have to wake up in the middle of the nigh to fight off a pack of wolfos, but it is freedom. No, they must not have known it, for they call him lonely, and on nights like those he is anything but. On nights like those, he thinks that he would do anything for the people of Hyrule, except perhaps share this single, solitary freedom with them.
They would not understand. They would think he must be glad for their company, for Din forbid that anyone appreciate being alone. They would talk of small things, or large things, but no matter the relative importance, their words would crush the fragile thread of freedom and solitude that twines itself around Link's existence.
There are days that he wants to be like other people. When the mental and physical exhaustion makes him want that bed, that fire, that family. When he wants to just throw himself into someone's arm's and sob. But for what? The relief would be temporary, and he knows that his feet would itch for travel, his hands for battle, in mere days after such an event. Link has many talents, but setting down roots isn't one of them, and it would be unfair to people to pretend it was. So, mostly, he fights, he wanders, and he visits the little hamlets and towns of Hyrule. He has pleasant conversations with the people there, and they admire and like him, but he never lets them see his weaknesses. Not because he is their hero. Because he knows that, if he did, they would expect more from him than he can give, and he does not want to let them down.
They know that he has weaknesses all the same, for though they are common people, they are not fools. But they do not understand the nature of his weaknesses, or that, really, at the core of it, Link's greatest weakness and his greatest strength is that he is so seldom lonely.