I'm a rather aware person, which includes self-aware, and it really makes me hate the non-aware because the idea of "I can just smile through the bad stuff" can be so false and harmful to not only the self but others that I think it's become one of our major problems as a society. Cognitive psych has its limits, it has a point where it becomes unhealthy.
BUT
That's not what that video was about. Choice does indeed add stress and can become overwhelming. Of course, the best way to fight this is to realize there is no perfect choice, that there is always room for error and failure, so that when whatever you choose is not the end-all be-all, it isn't a huge dissapointment, and it isn't that large a stress factor. You have to learn what is important.
So it's not really choice that is the enemy, but expectation. Having choice does not mean you will finally get exactly what you want, it means that you will get a closer aproximation to what you had thought you wanted before actually having the thing.