The Atkins diet was built on this premise. However, the high fat portion is not recommended by many health experts. The low carb is great. so to satiate we recommend GOOD fats such as avocado, nuts etc
The Atkins diet went off the rails because it also turned into high protein.
I'm started trying to get myself back into better overall health this year by going to a high fat diet.
Actually, not really high, but focusing on doubling my fat to protein ratio, and cutting carbs way down. Basically, a Ketogenic diet, though I don't focus on whether I am in ketosis or not.
As you said, good fats. Also with carbs, only good carbs. Take away the carbs I get that are fiber, and my carb intake is around 20-40.
To take this to another level, also working hard on making sure the foods I do eat not only fit this high fat, moderate protein, and low cab plan, I also focus on eating foods that provide all the essential vitamins and minerals we need everyday. The last part is the hardest part, but that part is tough for any diet.