Earlier quoted context omitted.
Why so?
Maybe I'm wrong, I'm a very causal user, but I think the only way to do it is to create a shape that covers the part you want to keep, and then do object -> set -> clip or something like that; it's not exceedingly awful, but it's not as smooth as clicking "crop" and dragging borders.
Also, there are not 2 workflows, one for rectangles and one for arbitrary shapes, which is a good thing.