I (along with most climbers) still feel fear though! But it's specifically fear of _falling_ rather than just fear of being high up. In climbing, that comes when you _lead_ past your point of protection (where your rope is attached to the rock), creating the possibility of falling >2x that distance. In big wall climbing you might climb 10-50 feet before placing protection, so you are risking a potentially very big fall.
In tower climbing falls aren't possible (unless you screw up the system), because you are always clipped into at least one point of protection. I'd imagine that it feels more grueling than terrifying for most people comfortable with the heights.
[0] https://en.wikipedia.org/wiki/Spring-loaded_camming_device
But there are still single points of failure. In particular, the rope. It’s not practical to bring up two full strength (single) ropes on climbs. Failures are very rare but do happen—generally because a rope is cut by a sharp rock.
Climbing is inherently dangerous, but accidents related to gear failure are extremely rare. The most common cause of death is human error (particularly on repels), followed by environmental factors like rock fall.
There's a saying, though, among engineers - they can fix anything but the nut behind the wheel!
The first climb, I got about 75 feet up. My body froze to the tower. I watched as I told myself in my mind 'go. Continue climbing.', and my body refused to budge. It was pretty surreal. After a bit of this back and forth I gave up and climbed back down. The boss told me "it's alright, everyone does that."
The next day I went up to the top of that one, 200' up. It's terrifying at times but it gets easier. It never got easy though, and I quit after just a few months. I thought about my wife and kids everytime I went up, and how if I splattered they would be devastated.
Pretty early on I dropped a nice Dewalt cordless drill. I was 150 or 200' up and I thought to myself "is that thing ever going to hit the ground?" I didn't even hear it impact, but could see it explode into a few pieces. Must have been a windy day.
I think you learn over time that you can trust the gear/ partner / your judgement and technique. But that doesn't make all fear related to climbing disappear. There are situations in which fear is appropriate and I've been quite scared in them.
When Covid broke my regular climbing habit. One interesting part of going back to it after a year or so of not climbing - I felt some fear of heights again.
It was mild fear, and didn't have me to hanging on extra tight or something. I remember the odd sensation of observing this fear in myself and thinking something along the lines "Oh that's weird, fear of heights - I don't remember the last time I had this."
Like a muscle, if you start training to be comfortable again it seems to come back quicker if you had trained it well previously. I guess fears have homeostasis too.