I just watched a nice Retro Report video about diets: http://www.retroreport.org/video/fighting-fat/
Point being, we know less about "the ideal diet" than we think we do. Different diets work for different people. Fat is not necessarily bad. Truly eliminating sugar sounds nearly impossible, even vegetables have some sugars in them. Our bodies make cholesterol.
Being vegan was an eye opening experience to me how emotional food is to people. I enjoy food, but I don't think it's ever been something I throw fits and tantrums about, at least not in the last 20 years. Being vegan was a science experiment with mixed results. People that go all in on whatever diet, more power to you. I understand the mental focus that having a specific rigid diet gives you might be worth as much or even more than the actual diet. That being said, I am not sure of any popular diet that eliminates vegetables. Seriously, if you go raw paleo vegan then fruit, vegetables and nuts are about all you can eat, and I've never even heard of anyone going on a raw paleo vegan diet. So eat more vegetables.