It's still important for everyone doing math to know that the convention is bad, though, even if it's not worth switching. Then it becomes clear in several instances that slight blemishes in the beauty of equations are of human origin. It also help you think of 2pi as an object.
Teaching this in the classroom could engage a lot of students that might otherwise be bored sh*tless of the regular curriculum. For those that do pay attention it could open their minds to a new way of looking at maths as a human tool rather than some universal law. It's a shame its taken me till freshman year and reading this article to make the connection that a 6th of a radian is a third of one quadrant. I can't imagine how much simpler this would have been to learn if it was 2pi.
