I couldn't be persuaded to go bungee jumping either for the same reason.
But I don't take the intent was to max it out and scare yourself to death. I think it means push your boundaries little bit by little bit.

I have a moderate fear of heights. I've discovered it in Utah at a Delicate Arch. There is a way to come really close to the arch walking over about 30 ft wide slightly sloping rock surface. It is not difficult. However when I stepped on it, it suddenly reminded me of those coin wells where you drop a coin in and watch it spiral into a hole. There was an increasing curvature of the slope and there was a hole there, an unseen drop. I suddenly had a feeling like the hole was sucking me in. I turned around, gripped the rock wall behind me and became totally paralyzed, frozen, I could not even articulate that I had a problem. Someone saw it stepped behind me pressing his body at my back telling me I can release me grip. I didn't think I could, I was histerical, totally irrational, but somehow I moved my hands, one at a time alonge the rock with this stranger's body at my back, till we made it back out. I mumbled "thanks" shaking all over.

I did not like that at all! I hated being limited that way. It gave me no pleasure to have to be rescued or to have to say no to life. This fear even developed in me getting dizzy and nauseous watching someone ELSE standing close to a cliff! I just found it intollerable, so whenever I can, I take opportunity to overcome the fear just a little bit. For example on one hike, I found myself fearfully creeping across a ridge (3ft wide path!). When I made it to the other side (like there really was ANY question of possibly falling off it!) I took a time and walked back and forth several times till I could walk without fear and tension.

I also took beginning climbing classes. Incidentally, many rock climbers also had fear of heights, and that is why they got into it. The class took place not in a gym but on a real rock, outdoors. Very real, very scary, except completely safe. I climbed and stood balanced on a 1/2 inch ledge on a rock, the support line hanging slack looking down at 30 ft of rock wall I just climbed. I would have been terrified and frozen if not that support line, but the line was NOT holding me, it was just supporting my mind - giving me knowledge that if I did lose balance I would be immediately caught. My partner below was watching me, the belay line was not going to slip out of his hand. I was safe, and with that I found balance and awesome sense of freedom. I still could not free climb that rock, but I knew that if I wanted to I could work my way to it.

It takes constant practice to maintain it. The less fit I am the less confidence I have in my body, and more gripping the fear. I have to feel my body's balance to release my mind's fear. I have to talk to myself, distract myself so the panic does not start. I found that forcing the mind to be completely focused on the present moment, calculating next step and not gazing into an abyss helps. Or talking to someone. I had someone "talk me through" a very scary looking climb down along the chains down to the overlook at the top of Yosemite falls - dude was just telling me jokes and entertaining stories, and it kept me from getting taken over by my fear. He too was one of those people who attacked his fear of heights, and became a climber.