Well we know that lack of circulating insulin usually leads to weight loss.. you just need to check with many T1's for whom one of the main leads for diagnosis was unexpected weight loss however much they ate.
This weight loss is a result of not being able to use dietary energy due to a lack of insulin. This causes the body to use its own body stores canabilising protein/fat whilst glucose is also poured in the urine if the blood sugars exceed the renal threshold. The weight loss could essentially be said to also be the result of a calorie deficit because much of the dietary energy isn't being used and or excreted out.
I have never seen controlled studies showing that lowering insulin causes weight loss and it is a very testable idea. Indeed, this has been done and the results showed that it didn't happen.
I am not anti-low carbohydrate diets at all, they clearly help people lose weight and better control their blood sugars - I just find the explanation for why they help not convincing. At a biochemical and physiological level it just doesn't add up. If it did I have no reason not to believe it - infact I once did and was very excited by the idea
You mentioned Ancestral diet, I wondered if the carnivore diet you use is what you consider this to be? It isn't an area I have looked at but I do not recall coming across diets consumed by humans that were zero carb at any point in our history (have you?) although animal foods would likely have made up the majority of the diet for various hunter gathered tribes. I believe even today, tribes closest to hunter gatherers consume diets with large amounts of plant foods. I'm not sure what % of your diet is protein, but if you are in ketosis I assume you are keeping it moderate however moderate to large amounts of protein will still evoke an insulin response. Despite a concomitant rise of glucagon, this will only help dampen the effect insulin has on glucose - the claimed deleterious fat building effects of insulin will not be abolished as far as I am aware..