While I'm not a proponent of Jason Fung or his book, I have read it. From what I recall, where your as-long-as-I-could-control-my-portions diverges from Fung's book is that he believes its nearly impossible for people generally to ignore their appetite in the long run, without correcting the issues that are continually increasing their "set point" and appetite.
He defines your "set point" as your level of secretion and resistance to insulin, which is continually, but slowly, increased by frequent meals, snacking, sweeteners, poor sleep, stress and consumption of mostly processed foods.
He believes insulin levels strongly influence appetite and metabolism. Inject a thin person with insulin, and they will invariably gain weight. Suppress insulin, and people lose weight. He lists studies to that effect.
He rejects calories-in-calories-out, not because it's false, but because it ignores people's inability to ignore their appetite in the long run.
His solution is both correcting the frequent meals, snacking, sweeteners, poor sleep, stress and processed foods. He also advocates fasting, which he claims is safe and reduces chronically high insulin levels better than any other (non-drug) intervention. He provides more studies supporting those assertions.
As to the 6 months, I vaguely remember him mentioning "6 months, or a year" in the contexts of most diet's plateauing effectiveness, but his general thrust was, most diet's don't work in the long run, because they ignore insulin.
To clarify, I am not Jason Fung, the author of the book that I summarized, and I specifically said I don't endorse the content. I only recounted it because ancestor comments seemed confused about the book's central tenant, which I happen to have read.
Strength training is one way to do that for example -- more muscles, more food burned just by sitting there.
Getting back to the perfect analogy with debt -- you can spend more or less money and control your debt that way, or you could make more, or a combination of the two. Which way is likely more effective in your case is what varies.
Saying that controlling debt is as simple as spending less than you make is both true and too general to be useful.