I'm guessing it depends on the kind of diet. If you want to loose weight short term and you watch what you eat or you follow a program, then the calorie gain from drinking diet sodas is great. Even more, you can have the occasional sweet thing without ruining the diet.
If you want a long term, mostly maintaining diet, then yes, the side-effects can become important.
And to answer your willpower question: yes, it comes from the brain. But we have many "brains". And the one you use in a strict, short-term weight loss diet has very little in common with the every day "I feel like having a snack and it's ok" brain.
I think this nails it. If you're part of a conscious diet and watching calories, diet soda can be a good choice, because you're _explicitly_ controlling for the effect the study is about - the false sweet causing cravings and ultimately more calorie consumption. It might follow, though, that the diet soda makes the rest of the diet more difficult.
If you're just subbing in diet soda for regular and not paying particular attention to overall diet, though, this study argues that you'll overall lose, as the diet soda increases your cravings for sweet and, left unchecked, you'll gain weight. Seems plausible.
(I don't worry too much personally, since I'm part of the population to which artificial sweeteners are not palatable. I'd rather drink water, and I do quite often.)
If you want a long term, mostly maintaining diet, then yes, the side-effects can become important.
And to answer your willpower question: yes, it comes from the brain. But we have many "brains". And the one you use in a strict, short-term weight loss diet has very little in common with the every day "I feel like having a snack and it's ok" brain.