I would be very surprised to find very many "normal people" who have the drive to learn, say, probability theory or statistics to any reasonable depth by self-study. Of course such people exist, but they are neither typical nor common.
Once you've been in the real world for a while, the idea of going back to school is generally the last option, not the first. The only thing school has to offer over self directed learning is very smart people to learn from, but if you look around, you can find those people in the real world as well. Mentors tent to show up just when you're sincerely looking for them.
On the contrary, many people take classes and attend conferences, workshops and seminars at many different ages. You could learn cooking by self study, but cooking classes continue to be popular, despite being more expensive.
The only thing school has to offer over self directed learning is very smart people to learn from
Hardly the only thing: a lot of things are easier to learn when you're in a group of intelligent people all interested in approximately the same thing, and all trying to learn the same subject matter (I'm thinking mostly of graduate seminar classes here, not 300-student undergrad lectures).
You second point just echo's what I already said, smart people to learn from, that includes your teachers and peers.
My second point was not just that you can learn from your peers, but that there is a social environment at a school that is important, and not readily replicated in self-study. You don't learn much from your peers at a typical cooking class, but they still contribute to why many people choose to take classes rather than self-study.
Yes, school is a social environment for learning, that has value, but it's hardly the only way to obtain that. Outside of school, there are local clubs and hobbie groups, forums and blogs such as this on the Internet, alternate paths such as the military, etc. There are all kinds of ways to be around people who enjoy the same things you do, or are trying to learn the same things you are without going to school.
By saying thats a benefit of school you're implying that it's not obtainable elsewhere. School just isn't that important if you really want to learn, it's more valuable for those that lack motivation and need someone to make them learn.
In what country? Citation?
Here's some numbers from the UK: http://www.universitiesuk.ac.uk/faqs/showFaq.asp?l1=2&ID...
According to that, 43% of 17-30 year olds enter higher education in the UK.
For actual numbers of people in the UK with degrees, there's this page[4] from the National Statistics. For people of Working Age, 18 to 60-ish, in the UK, 16% have degrees, and another 8.5% have "Higher education qualifications". 15% have no qualifications. It would be handy to have data for the 25-35 age range, since not many 18 year olds have degrees.
[1] Type A: http://stats.oecd.org/glossary/detail.asp?ID=5440
[2] Type B: http://stats.oecd.org/glossary/detail.asp?ID=544
[3] World Stats: http://www.oecd.org/dataoecd/17/15/39245059.xls
[4] UK Degree Stats: http://www.statistics.gov.uk/STATBASE/Product.asp?vlnk=10446