Sorry about the title. Couldn't help it, I swear!
TKD master Colin Wee takes on the Axe Kick in this excellent critique.
Money quote: "I once had a visiting black belt who used this particular axe kick frequently in sparring. None of our students could understand why - since it wasn't really hitting them. When I pulled her aside she said the kick was to knock someone out. So I told her to perform the kick, and I lunged in and took the downward falling axe kick right on my forehead - full force. Then looked her in the eye and said there's a problem with this kick."
His analysis seems spot-on. For self-defense, the axe kick is near suicidal unless performed on a downed opponent, but Colin's points about sport sparring are just as valid. So, read it all: http://www.joongdokwan.com/2012/06/axe-kick-risky-taekwondo-sparring.html