Firstly, as always, it's all about the execution. If you can pull it off, there's no reason why not to start in a contented place.
However, it might be harder to pull off. Discontent naturally creates conflict, aspirations, goals and motivation. The plot flows naturally from there. With a contented character, there is no reason for change, no reason to progress. One might pull it off by having some exposition sprinkled in, which would create adequate interest. However, this can easily border on info-dumps.
At some point, discontent should settle in. How early? Probably pretty early on, even in the first pages. Starting with a contented character, then having some incident which causes discontent, is actually pretty classic IMO. It might even help the reader identify with the character, since he/she is presented under "normal" (for the world) circumstances, before being thrown into the main conflict.
One pitfall I can think about, is making it seem forced. "Oh, look, Joe is having a great life. Better kill his whole family to make the story move forward." This is entirely dependable on the execution, as well.
In essence, I have no problem with the idea. Execution, execution, execution.