Technical difficulty of a climb is an important factor. On anything harder and longer than recreational slopes, a fall could mean certain death regardless of whether you have a leash, whereas loosing an axe (or ice tool) substantially lowers chances of surviving the descent.
Besides, the argument that having a leash makes it inconvenient to switch hands is weak since it can always be removed (or wrapped around the shaft) when ascending easy snow.
https://www.youtube.com/watch?v=NfpYNr7es0Y
