I think there's more to fear of heights than a mechanical issue. I used to have a fear of falling while climbing (an activity you need to get comfortable doing over and over again if you want to climb at your performance level) and the way I solved it is by going to a rock gym, twice a week for over a year and taking decent falls on purpose.
I believe getting over fears through exposure can more profoundly change what a person fears. Even if this works, what if you lose your head gear at the pinnacle of your alpine trip?