Also savannah human diet is chock full of fiber too: baobab pulp, grass seeds, tuber plants, etc
You just have to look to the belly of a healthy, non-obese human and compare it with the bellies of the apes. The bellies of the apes are much bigger, despite not having the fat of humans, because they have much longer intestines, which are packed in there, which are required for the fermentation of the large amount of fiber included in their diets.
The intestines of humans are not so reduced as those of the obligate carnivores, but they are still much shorter than of most apes or monkeys.
Our health is still dependent on eating a decent amount of "fiber", but the amount we need is not comparable with what an ape needs.
My point is just modern diet is severely lacking in fiber, when our gut evolved to process them.
It's not a surprise this evolutionary mismatch will cause so many problems in our body.