I think people do learn in school. Humans are learning machines - we'll learn whatever we can, wherever we find ourselves. So, we do learn in school. That's the issue behind this thread on the schools being failures even by their own measures - the 'writing' part of reading, writing and arithmetic seems, even as measured by the latest test results from within the educational bureaucracy, to be sorely lacking. If the people who care about you read, learning to read is almost as automatic as learning to speak.
Basic math is a little tougher, but can be mastered in an hour or so a day spread over a few months.
Writing, as Mimsy pointed out, requires thinking - hard to see how that figures into the classroom model. I could see, maybe, sending a kid to school for 6 months, max, to learn these things, if the teaching were demonstrated to work.