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?

Likewise, beekeepers often lose their fear of bee stings just by being stung so often. They say, "eh, that wasn't so bad".

My fear of heights isn't about balance, but about being in high, exposed places.