Your mishap in the chute underscores the necessity of a leash. An ice axe without a leash is just an expensive toy that a hiker loses while falling to his death.
The owner of "International Alpine Guides" (one of the Sierra guiding services) told a horrific tale of someone getting impailed by a leashed ice axe. From my rememberance, the ice axe stayed embedded in the climber until a helicopter got the climber to a hospital. This is why I believe guiding services do not like leashes. That being said, I am too mindless not to have a leash. I am extremely likely just to mindlessely drop it on a steep slope and watch it rocket down the mountain. So its skewering for me.
