I doubt ape society is just and wonderful,
but that is what we are "designed" for.
Stratified, competitive, cooperative,
ageist, sexist, and suspicious of
outsiders. Led by an alpha male.
That view of apes and humans was once quite popular even in scientific circles. I think that it still enjoys some popularity outside of scientific circles even today. However, it is contradicted by a considerable body of evidence. There are today no or almost no specialists in the field who believe we evolved to live in stratified, competitive, ageist, sexist, societies led by an alpha male -- although some would agree with you about our evolving to be "cooperative" and "suspicious of outsiders".
If you're curious about the consensus thinking in the field since the last half of the last century, here's a bit more on it. Or you can google up much, much, much more on your own.
John Rawls on the Fair and Just Society