The thermic effect of protein is pretty much negligible, and food restriction has also been shown to not be the obvious explanation in trials where they partitioned out exactly the same amount of food (2000 kcal, I believe) in different ratios to find that the lower-carb apportioning caused the greatest weight loss.
In short, whatever facts anyone wants to bring up, there will always be more that either disprove, or at least throw them into doubt. But your final point is absolutely spot on -- it is absolutely about what works for your health and your situation. I've found low carb, unprocessed (i.e. paleo) with a sprinkling of IF and cycling works great, but I don't intend to be a militant defender of this approach; rather, I absolutely advocate n=1 experimentation, figuring out what works for you, and doing something rather than nothing. Learning about paleo kicked off a huge revelation in terms of my personal health and I want others to discover this joy.