Is a "mostly meat" or "low carb" diet helpful for weight loss?
No way! Any diet that's based on consumption of only one food or type of food, or that routinely blocks you from modest helpings of all six food groups is unhealthy over time.
What are you going to do after you've gone on an all meat diet, and then go off of it and return to your old eating habits?
I believe that God gave us a variety of foods for good reason, and we should enjoy that diverse bounty. We need vitamins and minerals from vegetables and fruits, roughage too, to help with digestion. We need grains for quick energy. We need dairy or foods with calcium in order to prevent osteoporosis (brittle bone disease that many older people are susceptible to). There are anti-cancer properties in many yellow and green vegetables.
Not to mention that a diet of all one thing gets really boring over time!