That becomes clear when you look at the "caveman diets" that are recommended for people with really radical food allergies. (They're allergic to just about *everything* in the modern diet - wheat, corn, soy, milk, you name it.) The "caveman" diet consists of lean meat (as close to game as you can get - lamb is about the most basic), nuts, some leafy greens, and low-glycemic, low-sugar fruits like blueberries, strawberries, concord grapes. Cavemen also got a lot of fat & vitamins from grubs and insects, but that's not on the menu, so other fats have to be added too.
People didn't start eating tubers and roots until there was the technological capability to boil water (i.e. baskets or clay pots that could stand the boiling process.) Raw tubers are generally undigestible, and others like carrots are the product of agriculture and selective plant breeding.
In other words, for hundreds of thousands of years we didn't eat high-carb foods at all; it's really only been in the past 30,000 or so that we've most likely boiled water, and only in the past 6,000 or so that we've eaten cultivated grain. The body just hasn't caught up.