I also don't see why being noble is a problem, especially in DAI, where things are not defined and you can play as a black sheep of the family and generally very few characters in the game give a damn.
I'll try to explain, as long as no one takes it personally like I'm insulting their characters.
I prefer the arc for Lavellan from beginning to end. Mine is a mage, so for a Dalish mage, waking up in a human prison surrounded by templars is like her worst childhood fears come to life- plus a giant hole in the sky. She has the surreal experience of being proclaimed Herald of Andraste and of coming to the rescue of people who will always hate and mistrust her, as demonstrated poignantly by the Dales. And all of this is apart from the revelations in the game about elven heritage and the fact that Fen bleeding Harel was her companion and lover. At the end of the day, you do the exact opposite that everyone expected of you, and became a hero.
With Trevelyan, you're from a privileged family and sent to the Conclave because mummy and daddy said you had to serve the Chantry. A mage has more stake and is also an underdog, but not nearly as much as a Dalish character, plus you spent your whole life in a Circle so there's not a lot to work with in terms of back story. And at the end of the day, I find myself thinking "great, I'm one of the boring assholes who run southern Thedas, and I've just affirmed their opinion of themselves as being the rightful rulers of the world. Yippee." It just doesn't work for me.