I did this years ago and lost some weight doing it at the time, but the basic premise of "a calorie is a calorie is a calorie" is provably not true. The body's metabolism plays a massive part in determining how many calories are consumed, and this in turn is driven by availability. Long term calorie deficit will result in your body learning how to operate more efficiently, and slow down your weight loss.
I've also tried low-carb twice, the first time I lost a reasonable amount pretty quickly, but gained it back over a few years when I reverted to a normal diet, and the second time when I shifted to intermittent fasting as I went back to a more normal diet.
There's lots of good advice available if you search for intermittent fasting, but the key take away is that insulin is produced in response to excess carbohydrates, and not only promotes storage of carbohydrates as fat, but also inhibits burning existing fat. Of course, if you are at a calorie deficit, you'll probably still lose weight especially with regular small amounts, because the insulin effect will be low, but if you have few carb-heavy meals, your body will still create a lot of insulin to get rid of all the carbs, and then after you work through the hunger phase after that's happened, then you will start converting that fat back to energy, and in a calorie restriction situation hopefully burn more than you need.