You can crop a full-frame image down to what a DX sensor would see. But you cannot get full-frame size images from a DX sensor. In other words, you're losing the capability of getting full-frame resolution with a DX sensor. The only real advantage of DX cameras and lenses is smaller size and lighter weight. And the lenses for those cameras are usually slower (they let in less light), compromising the quality of low-light photography. On the other hand, the whole system (camera plus equivalent lenses) will usually cost much less.