You are completely right it's surprisingly difficult to out exercise your mouth! When you do these calculations just remember to include the basic metabolic rate.
You are also right diet is the most important factor. You've got to eat less than you use.
However exercise causes you to expend more energy and even a small energy deficit will lead to weight loss over time.
Another important factor is that exercise helps to regulate appetite.
I personally think the increased appetite from exercise more than cancels out the benefits to weight loss. I've also read that before but I don't know if there is a really good study to back it up. Don't get me wrong, I think there are a zillion good reasons to exercise but losing weight will never be one of them.
You are also right diet is the most important factor. You've got to eat less than you use.
However exercise causes you to expend more energy and even a small energy deficit will lead to weight loss over time.
Another important factor is that exercise helps to regulate appetite.