Raoden was never really in trouble.
You don't consider it trouble to go from being a very popular prince to a hideous bruised Elantrian locked in a decaying city populated by madmen? Or to cope with constant and increasing hunger and pain? Or to convince hordes of crazy people to regain their sanity? Or to see all the amazing feats you've accomplished unwittingly undone by your wife? Or to be given useless trash in place of the materials you need to build a civilization? Or to lose your general to madness when he's following your orders? Or to have your closest friends not recognize you? Or to have your people attacked by monstrous beings trained to kill? Or to know that your kingdom is being undermined by a foreign power, and be unable to do anything about it because you're locked away?
Perhaps what you mean is that Raoden triumphs over each of these problems. But that doesn't diminish the problems, or make them less real; rather, it makes him more admirable. In real life, would you say to a cancer survivor that his cancer was never really a problem because as it turns out, he overcame it? Or to the scientist who discovered a vaccine for smallpox, that smallpox was never really a problem? Or to an Olympic gold-medal gymnast that her accomplishment is meaningless, because she won? I don't know about you, but I admire these people, I don't find them or their achievements boring.
Similarly, I don't think that a character, even a main protagonist, needs to fail occasionally to keep my interest. I like watching Raoden win, watching the creativity and inner strength with which he surmounts each obstacle and recovers from each setback. After all, he doesn't win all at once - it takes him the whole book, and a whole lot of study and practice, to figure out the AonDor problem - and even then, his first success is only partial. It also takes him most of the book to coalesce the other Elantrians around his cause - and again, there is the setback with Sarene's Widow's Trial. Just because he wins in the end doesn't mean there is no struggle (and apparent failure) in between, to get there.
So I'm going to stubbornly hold to my opinion that Raoden is my favorite character, even though I'm aware that this isn't considered a sophisticated opinion in literary circles. You're not supposed to like the good guy best, the bad guy is supposed to be your favorite. In order for you to like the good guy, he has to do something bad or stupid. Well, I don't think that's true in real life, so I don't see why it should be true in a story.