When walking over it, the Karnute also removes the tree stumps. This means that nothing can grow back. I have many places in my floating world where it runs over where there used to be trees, but now there's nothing there at all. And the Karnute only removed them when it ran over them.
I'm glad someone else said this. I thought I must have been imagining things when a grove of trees I was re-harvesting after the carnute went by and noticed fewer and fewer trees each time.