Contemporary Education

Education teaches facts.
It also teaches the hidden curriculum. how to be punctual, how to be social, how to respect authority, how to live in society once you are an adult basically.

So yes, of course it has intrinsic value. If I had never gone to school and had only been home schooled I never would have made friends, I would have grown up sheltered and would have been unprepared for the real world.

To a certain degree, and certainly only to some. I know several people who have missed out on those lessons.

And to very roughly quote an old, meddling headmaster, "the value of Hogwarts doesn't come entirely from the lessons taught in classrooms, but also in the lessons we teach ourselves." (Mind you, that may be a quote from and fanfiction Dumbledore, but it still applies.)