It depends on what you count as a "successful diet"... If it's about losing fat, one can lose fat on an all-junk-food diet so long as they keep their calories in check. One could also consider gauging the diet by the foods you eat, and there is truth to some being better than others in that regard.
But what I believe is the ultimate measurement of the success of a diet, is how the individual feels while on said diet.
If you feel deprived, "hangry", out of control around foods you shouldn't have, I very much don't see such a diet as successful, even if it consists of foods that would make up the perfect ratio of everything a human body needs to function perfectly.
On the other hand, if one would feel satisfied, satiated, and in control around food, but eating a diet strongly deficient in X,Y,Z nutrients, that would also not be a prime example of a successful diet.
I believe that for a diet to be successful we need to take care of both aspects. Have an individual feel good, in control, with plenty of options and without restraining them from having X food(s), but also have this diet be balanced in terms of nutrients.
It may sound hard to achieve, but that's mostly due to the marketing/media.
Also, "cut the crap"... the "crap" here is, what, exactly?
Cake by itself isn't bad. Cookies, ice cream, pizza, and so forth aren't bad either. They are calorically dense foods (often with little to no micronutrients), but they aren't the real culprit. You can have them all, so long as the rest of your meals stay inside of your caloric range and not gain fat.
Think about it, near all diets have a culprit, a demon, something that's responsible for everything bad. Some say sugar is bad, some say fat is bad, some say you can only ever drink kale juice and nothing but. But it's really, really, not as simple as that... Or as complicated, depends how you look at it.
All foods can be enjoyed without the guilt so long as you know how to make room for them. Eating one cookie won't make you fat, but damn, a whole packet probably might.
But we've been ingrained with this image of there having to be an enemy, a culprit, something we need to demonize and avoid at all costs, when in reality, it's just... really not like that at all.
What I'm, in short, saying here, is that, Yes, most of your diet should consist of whole foods, but if some of it is highly refined and/or what most classify as "junk", that's okay too.
There's also a full chapter on labeling food as "good" and "bad/junk" is harming you more than it does good, and also why having "cheat meals" is likely not your best idea.
Anyhoooo, I'll stop this wall of text here and thank you for stopping by! :D
RE: Do I Really Need Another Diet? - A psychological approach to your relationship with food