Actually, my partner has been keto for over a year now and the reason that you lose weight on high fat is because your body doesn't need to store the energy gained from carbs anymore and can simply go after the fat you have stored on you already which is more accessible. You run on one of the two - fat or carbs - taking carbs out of the equation means you're going to burn your existing fat when your body needs energy instead of you needing to go and eat. There's lots of proven science behind it, and it does work, but it needs done properly. It is actually sustainable in the long term as well, carbs aren't an essential thing that you really really need or I'd know a lot of people in a sticky situation!
His grandmother has been doing it very successfully as well, along with a pretty decent number of friends. If you get properly into it you can still have a lot of treats too, just need to make them yourself. The initial loss is water weight true, but it does seem to have quicker results, and it can feel pretty rubbish at first as you adjust to not taking in sugars to run on anymore, but it seems worth it. I just don't adapt well and don't have time to do it or I would!