Related questions:
Some fatty acids are essential nutrients, you cannot synthesize them. There are 10 important fatty acids, 2 of those are absolutely essential and 2 more which are highly desirable (because their synthesis is very inefficient from other fatty acids). Many non-meat sources are rich in these (vegetables contain fats too).
You also cannot efficiently absorb vitamins A, D, E & K without dietary fat and will likely be deficient in them if you don’t consume them via meals that include fat. Fat is also a valuable source of energy, your body prefers to use fat ahead of protein as an energy source.
Eggs are a good source of fat but not of essential fatty acids. The best sources of the essential fatty acids are oily fish, nuts and vegetable/seed oils.
Being even deficient in fatty acids, particularly omega 3’s, will cause cognitive issues.
Most recommendations I’ve seen say to keep it at 15-20% of calories from fat, but less than 10% of calories from saturated fats and as few trans fats as possible.
https://extension.psu.edu/fat-facts-the-right-amount-for-a-healthy-diet