Yep, my neighbours keeps goats next to my propery, they escape once in a while. They go directly to the soft greens in my garden. When the fences hold they eat the area clean by type as you say. First the grass, then the leves of the small trees, then the bark (killing the small trees). Only when there is nothing else left will they eat the nettles.
I'm not familiar with goats. But this got me thinking: why would the goats even do that? Are they not well-fed? Are they hungry all the time? Do goats eat and poop 24/7 if left unchecked?
Yes. Many grazing animals are like this. It's like they have no "feeling full" in their tiny brains. Grass and leafs are not very calorie dense so they kind of have to.
Cows or horses can easily eat themselves sick if they are let into high grown grass fields. Where I live the horse owners will sometimes cut the grass in the fields before they let the horses go to it in the spring.
Not animals you want around flora you care about.