It's not the height that makes you dizzy - it's the swaying. Imagine how much a building sways but you don't really notice it because the swaying is pretty slow - but the swaying can be faster on a thin antenna.
What's creepy is that the first time you're up there and the thing starts moving, you don't know when it'll stop moving and so you think you'll fall off the thing before it starts swinging the other way. It's extremely disorienting.
Made it to the very top before freaking out. Good god.
Also: there are perfectly workable fall-arrest systems that can be integrated into ladders that don't require constant hooking-unhooking. Why they're not being used at this point is beyond me.