It is an interesting question. Although, you do have to differentiate between learning skills and an actual education, which I take to be an improvement in critical thinking and general overall awareness.

I still think there would be interesting problems to solve, even in a perfectly educated society. I don't want to be a brain surgeon, or any surgeon, or anything really in the medical field. There is a theory that some people are "naturally inclined" to certain tasks and maybe we could realize that and have a society that allows everyone to specialize in that...