William Godwin's Philosophical Anarchism

My knowledge of the topic is very shallow (this was William Godwin's thing right? or do I have even the name wrong?) but from what I understand of it, in summary he believed that as knowledge and education spread across to all people, that government would be obsolete. (right?)(maybe?)

Now after thinking about this for awhile, I've come to agree with him. But the thing is, education has spread, and we still are nowhere near capable of anarchism.

So my question is are we being educated on the wrong things? In school we learn about the chemical makeup of cork and equations for calculating polar coordinates, but do these things help us in life? (my answer is very much no.)

If we were educated on spiritual and philosophical things rather than industrial and scientific, would we be able to rid ourselves of government? Any person with an education in ethics or logic would be able to conclude that killing is wrong not because the law says it is, but merely because reason dictates that it damages society on multiple levels.