That's a good question.
In the past, I've tried to merely restrict calories and eat what the food pyramid recommends... plenty of "healthy whole grains" and limiting fats. I lost a tiny bit of weight and was miserable and hungry - and my cholesterol numbers actually got worse. I went to the gym every day but was tired and listless mosf of the time. And as soon as I eased up, I gained even more weight (over the equilibrium weight I was at before starting the calorie restriction).
If you look at how metabolism works, fructose is only processed in the liver and the result is serum triglycerides. Dietary fats, however (at least as I understand it) are quickly taken up by chylomicrons and delivered to cells throughout the body, so they don't contribute much to trigylcerides as measured in the standard lipid panel. This is at least how I undersand it.
My personal experience is just an n=1, but within the low-carb community, the predictions were that by adopting a an LCHF diet, I would lose weight, not be hungry but eat less, feel more energetic, and that my lipid panels would improve. I've found all of these things happened, as well as odd little things like no longer having indigestion and just having a desire to exercise and be more active.
Do I KNOW this is from an LCHF way of eating? Not with absolute certainty, of course. But my experiences match the predictions and when I do endulge in a large amount of carbohydrates, I tend to feel not-so-great for a couple days.
Frankly, I'm just thankful to have found a way of eating that allows me to lose the weight I've carried for decades while allowing me to be more energetic, and with all that, not suffer from hunger or feelings of deprivation. A year ago, I had conceded to my best friend that I would always be fat but I could at least be active and fat (I was already bike-commuting and hiking). But after a mere 8 months of this way of eating... eating "as much as I feel like eating", I now weigh less than I have in almost 2 decades and I've started racing (albiet slowly) in 5Ks and triathlons. And note, I adopted the diet and started losing weight (about 30 pounds) before I started any of the running.
Maybe it's a "fad diet", I just eat like diabetics were told to eat in the early 1900s (https://archive.org/details/diabeticcookeryr00oppeiala) and how like most people were told to eat to lose weight until the 1960s or so. It's essentially "meat, eggs, and green veg" but avoid sugars and starches and most fruits. And I've never felt so good as an adult.
So my n=1 is not "science" and maybe it's all placebo, but if so, it's a pretty darned good placebo. I'm down 60 pounds I never thought I could lose and doing crazy things like triathlons, which were also unimaginable, even a year ago.