Ingredients like sugarcane extract, fruit extracts, mixed fruit extracts, and milk solids may claim an association with AHAs, but they are not the same thing nor do they have the same beneficial effect on skin. While glycolic acid can indeed be derived from sugarcane, if you assume that sugarcane will net you the same result as glycolic acid, that would be like assuming you could write on a tree the way you can write on paper.
Wood is certainly where paper begins, but paper wouldn’t exist if the wood didn’t undergo complex mechanical and chemical processes. Similarly, the original forms of these extracts do not have the same effect as the ingredients that are derived from them. The same is true for lactic acid, derived from milk. There is a vast difference between the extracted, pure ingredient and the original form of the source material.