My DD was 11 days late. I was due to be induced at 10 days over but chickened out, went into labour and she was born at 11 days o/d. Labour was augmented, without augmentation she probably would have been born at 12 days over.
It would be interesting to see how many are born before vs after their EDD. I wouldn't think it would be 50/50 though because there is a much longer time in which a baby can be born prematurely (15 weeks or more) as opposed to overdue (eg you never hear of a baby going 15 weeks past their DD).
I think the reason for induction for post dates is that there are some studies that show an increased rate of neonatal death at 41+ weeks of pregnancy.