The phenomenon of school where you have a lot of people of the exact same age together is a relatively recent experiment. I'm not sure it's of the natural order of things.
People in the past would have learned as apprentices and journeymen, learning from those older than them. There would have been more heterogeneity. Going back further, hunter-gatherers would not have stratified by age so distinctly.
School now is also rather unique in how it is so long of duration, both of the day and the years. There are a lot of groundhog years between kindergarten and 12th grade where you're treading over similar material and the medium of school itself becomes fodder for an entire industry of teen movies and television shows based on school culture (90210 etc) rather than a practical tool to a particular end. Look at that 13 Reasons Why discussion where we discussed that. Look at the Kavanaugh hearings. Regardless of anything else, it was clear those kids spent their years in high school like some high-brow version of the Jersey Shore. I think it's a rather inefficient use of time (as well as undergrad repeats so much of it for those who worked hard in high school). I think the inefficiency is baked into the point of the system in that our society has nowhere else to house children and no better ideas. But I don't think it is an ideal system. It seems to 1) lack a clear purpose for many people who enter into it (and virtually everyone enters it) and 2) not go about achieving results in any reasonable amount of time.
Eh, I don't disagree with all of this, but as I said, some version of throwing kids together for quite some time and them just having to deal with each other, actually does happen in most cultures, and has essentially been the rule ever since societies have grown beyond the band stage of development and further into tribes or chiefdoms, and beyond. So I don't claim that it's been a big factor in our actual evolution as a species on a genetic level, most of our time as a species being spent in small hunter-gatherer bands, I will say that it absolutely has been a feature of our
societies as they have grown beyond that point, and particularly with the advent of agriculture.
It absolutely is noted in most cultures that children do indeed choose to stratify themselves based on both gender and age - it does not appear to be purely a cultural construct or something that is imposed upon them by adults. Indeed, it would appear where this does not happen that it is more owing to constraints in the way that people in a culture have adapted to specific demands of the environment (such as the Inuit, or other cultures that must operate in very small family bands where there may not be a large group of similarly aged young peer groups)
OK, so I will take this back to say that there are not biological determinants in the observation of how members of our species aggregate by age.
Indeed, where this is most seen is in the development of male "gangs," which you observe even in lions and chimpanzees, and very much in humans as well. Given the combative nature of such groups, and the believed adaptive value of male aggression, these groups not only form but form amongst equals in physical development, ie often similarly aged peer groups.
The emergence of young "male gangs" in some species does actually appear to be part of the natural order of things, and it makes perfect sense.
Young women are also often grouped according to physical development, and indeed, menarche and where women are in their reproductive life cycle is often marks one's membership into different groups stratified if not by age, then by reproductive status, which tends to be a function of age. Young girls are also similarly grouped together, and rituals related to "coming of age" are common, and not only mark a particular day or events, but one's transition between groups.
Such groupings of males, females, and by species' development in the life history, is seen in many, many species, and in birds and primates, two species that for various reasons are relevant to studies on the life history of humans.
While it is true that our society is noted by an extreme stratification amongst members by age compared to other cultures, in that you are correct there is more mixing in other societies, even in your example where you have younger members mentored by older members, this also frequently happens in groups, ie a group of younger members together. The examples you describe occur more frequently in groups with a lower population density, such as the Inuit described above. A perfect example is in medieval Western Europe where you had the classic journeyman/apprentice structure, however this also gave way in the post Black Plague population decimation, as the population density rebounded and there was an emergence of the classic guild structure for education, which was also stratified by age. Also the ancient Greeks had an older mentor/protege dynamic. However, in the history of both regions you also see the emergence of "schools" and other groups stratified by age.
No, my friend, I am sorry, but you are wrong, it is the most common cultural observation for members of a society to quite early on be sent from the basic family group structure (away from home, essentially) to interact outside the home, in groups that are typically stratified by age, ie within one's own peer group. This has in fact been the norm ever since a given group has been large enough to have a peer group to speak of.
You could argue this wasn't a factor in our evolution and has been just a modern adaptation, but I think that ignores observations that are cross cultural, appear to happen without adult input, and also if you look at evolutionary psychology, and the parallels with animal development group dynamics.
I am in no way arguing for any given type of age stratification structure and its adaptive or maladaptive utility, just that the existence of such, and in the form of "schools" or "gangs" and in adolescent groups, is fundamental to many species, ours included.