I used to crave fats too (and sugar), but hardly do anymore as long as I'm eating enough on my high-carb/low-fat diet.
As for plant-based diets, the biggest mistake is under-eating and it's why I think a lot of people gravitate to wanting to eat a lot of high-fat foods, like nuts & avocados, is because their body is craving calories and fats are very calorie-dense. It's also why a lot start craving meat after awhile. Meat is very high in calories, but unfortunately the wrong kind of calories.