Ok, I have replicated the issue and now I think I see what’s happening: most probably you’re using
Fast Export Options > Processing pipeline > Dedicated
and the Maximum size indicated in the Resize part is bigger than the cropped size of the image.
E.g.: the cropped image measures 300x400 pixels, and the Maximum width and Maximum height are bigger, say 1500x2000 pixels. In this case the exported image has the same size of the raw file, with the crop at the top left corner, and everything else is filled in black.
Most likely this is a bug, but a workaround would be using
Fast Export Options > Processing pipeline > Standard
and unselecting all the Processing steps to bypass
Hope this helps
P.S.: by the way, in Batch Export cropping and resizing are two completely different things.