Agree with you Carang. The other thing a lot of people don't like to hear is - it's pure mathematics. If input exceeds output -> fat storage.
how to decrease fat storage? either decrease input, or increase output, or both. modify the input/output balance once body condition is at "ideal".
I generally recommend cut calorie intake by 50% (cut food volume in half, but meal frequency stays the same) until a good condition is achieved, then increase intake a little to prevent furhter weight loss, decrease it again if weight starts to go back on. It's not rocket science!
there's no magic food or diet that will make a big difference, a lot of dogs on low carb foods eat more of it and don't lose wt. some low carb foods are higher in protein (note, energy yield per gram of protein is the same as carbs), and others add fat to make it palatable.
easier to stick with the same food and cut it back.