I find the same thing. I don’t, at least not always. I think it differs from person to person.

I only went climbing less than a dozen times, so I can’t be sure about “getting used to it”, but then again Hermione probably wasn’t used to dropping from castles.

When I climb a “simple” vertical wall I don’t get any vertigo or other “lizard-brain complaints” as I had expected. (I rarely get vertigo from heights in general, and among my friends I’m usually the guy closest to any ledge, with everyone telling me to get back, from a safe distance.)

However, I did once a climb an indoor route (not sure about terminology) that wasn’t just vertical, it had a kind of lateral transfer to a ledge at the top, and the part where I didn’t see a wall below me all the way down did feel like having butterflies in my stomach despite being tied to a rope. I liked it, but I can see it as a very unpleasant experience for a bookish (i.e., not a tom-boy) 11 years old girl.