I would probably refer to that as "the point of sending your kid to school". Note that this is different from "the point of running the school the way it's currently run" (which is how I would probably interpret the bare phrase "the point of school"), and also from "the point of maintaining compulsory education laws".
It may also be different from "why parents choose to send their kid to school", because parents' perception of their choices may be incorrect—I think it often is.
And, of course, it'll be different for different kids. You say "the average", but as some say, the average human has one ovary and one testicle; taking an average across disjoint groups may not make much sense. A high school diploma is one of the most cited reasons for going to high school (not K-8), but that would really only matter if the high school itself is a brand name, which is rare (you probably have to be rich, talented, or lucky to get in); otherwise a GED should work equally well for college. For the upper middle class trying to get into elite colleges, an upper middle class high school will offer plenty of extracurriculars with which students can pad their applications. For socially adept poor kids that manage to live in rich districts, mingling with the rich kids may be useful. For kids with terrible home environments, school may be a decent escape. For kids that fit well into the social environment and aren't bothered by all of school's problems, it may be fun, good for making friends, and even a decent educational option. I think most of the above groups don't overlap much (except the "socially adept poor kids" obviously "fit well into the social environment"), and forming a picture of school's "average target student" wouldn't look like a real student and would probably mislead more than enlighten.
For kids in reasonable home environments, who are irritated by school's problems, who have friends and sports or other group activities they do outside school, who have access to libraries and now the internet and Wikipedia and free online courses, which are getting better while school seems to get worse due to its cancer... it's probably not the best choice (the kid's individual traits like motivation and curiosity may be deciding factors here), and as trends proceed that will become more clearly and generally the case. Parents' impressions of the available options are probably decades out of date.
As for the incentives that face parents themselves: for many, public school is primarily publicly funded daycare; for some parents, there is no reason other than avoiding punishment from truancy laws. Honestly, I suspect the strongest motivators in practice are social conformity—not sending your kids to school would be shameful or weird, make you stick out and become a magnet for criticism—and ignorance of alternatives.
Most haven't heard of unschooling, and probably think homeschooling is for Christian fundamentalists who hate evolution, or for geniuses; those who know more still usually assume that it requires a parent to act like a full-time tutor, and haven't considered options like "set up books and textbooks and ask your child once a day what they learned and if they have any questions". Some have thought that far and think their child would never be productive without constant supervision; the homeschooling advocate's response is that your child has spent years being taught that "education" = "adults imposing boring unpleasant crap on you", and it may take many months for that to fade away, but their motivation should improve eventually; still, it seems possible to me that there's significant intrinsic individual variation in motivation and curiosity that would make the difference.
It is disappointing when adults assume the worst about their own children and knowingly condemn them to years of misery; they could be correct, but what a thing for a parent to believe... One can also ask: if you really believe that, then how do you expect them to do well in college or in a career? Maybe they assume the motivation will automatically improve as the frontal lobe finishes growing (which is possible), and that faking it until then will get them into a place where they might develop hitherto unseen qualities and do well. To which I merely sigh, shake my head, and say life should be so much better than that, and for many reasons it's worth the risk of trying it the right way.