This is too reductionist to be useful imo. All nuts and seeds would be immediately disqualified. Olive oil or butter and most cuts of beef and probably there are more stuff that don’t come to mind would also be excluded. On the other hand, glass of milk mixed with 30 grams table sugar passes as healthy.
No. I think that even today, there is a misconception that fat is bad for you. It depends on the type of fat. If you eat unsaturated fats like avocado and olive oil, you can definitely eat quite a lot and still be very healthy. These concrete “barriers” are not good when it comes to food and nutrition.