Inverting crop selection would be useful in removing black bars from letterboxed images, for instance:
You are mistaking the Crop tool for a selection tool. It isn't. There is a Rectangle selection tool for this, and the selection it creates can be inverted.
Now, on your image:
- If you want to restrict the image to its center and remove the dark margins, then you use the Crop tool, and there is no need to invert the selection.
- If you want to delete the dark margins without changing the size of the layer image, then you use a Rectangle selection on the part you want to keep, then
- If you want to keep the dark margins, then you use a Rectangle selection on the part you want to delete, then