Not so much. Recent isotope analysis of the bones of our ancient ancestors show that for 99.9% of human existence, we ate a diet very low in carbohydrate and very high in animal products. Before we started hunting and butchering, we ate the leftovers of beasts that killed other animals. Carnivores typically don't eat much beyond the internal organs of their kill. We ate the rest.
We did eat some plants, but our digestive system evolved away from digesting plants to one better-suited to eating meat.
You are right about fiber "filling you up." But I never understood the desire to fill up on something that provides no nutrients. The point of eating is to take in needed nutrition.
And there is no such thing as an "inadequate amount of fiber." Fiber is a carbohydrate (and an undigestible one at that), and carbohydrate is a non-essential nutrient for humans. Our daily minimum requirement for carbohydrate (and, hence, fiber) is zero grams. The current recommendation for fiber intake came from the same place fiber leaves our bodies...
What's really interesting is that when you cut carbohydrate from your diet, you soon start getting energy to live from body fat. That's why low-carb diets work so well for losing excess body fat. This article explains it:
https://medium.com/illumination/the-key-to-keto-fcc2cfe2f7f9
In a nutshell, a low-carb diet triggers a shift in how the mitochondria in our fat cells metabolize nutrient energy when producing the chemical energy our cells need to do their work (called ATP). This shift causes our fat cells to waste fat and produce more ATP than our cells need. This is why you can continue to eat the same number of calories as you did before moving to a low-carb diet and still lose body fat.