Yes it does work and for most people, if followed properly and sensibly, it's a very effective, delicious and easy way to eat.
If it doesn't suit you, that's fine, you do what works for you. But frankly I despair at a society wherein GPs are paid to recommend WeightWatchers, with its reliance on buying expensive, sugar-laden, processed foods, and yet those of us who go for a low-carb way of eating (ie veg, meat, nuts, eggs and dairy, fruit in moderation) are called stupid and faddy... But there we go, shows what a fucked-up attitude we have to eating.
Lowcarb diets are precisely that - LOW carb, not no carb. My brain functions perfectly well, thankyouverymuch, on less than 50g of carbohydrate per day (mostly from veg - why people think low-carb means 'cutting out a food group' baffles me). It's when I have more than that that I feel foggy, tired, irritable, bloated, etc.
I love low carb, but if people want to carry on eating low fat tasteless cardboard shite that's their lookout - just means more steak with garlic butter for me!