Without doing a crosscut, you have no idea if you have removed the previous lines. Thus you would either be spending more time and material cost than necessary and/or these coarser lines will show up later in your procedures. Causing you to redo the item, wasting more time and material, not to mention the frustration. Missed imperfections usually show up when you get to your buffing procedures.
Another common practice that will void your advantages of a crosscut is using a DA or orbital sander. These will make small circular line patterns that make it next to impossible for you to see line removal from one grit to the next. This practice works great for auto bodywork, though, not for polishing and buffing to a mirror finish.
On the left in (Fig 2) is a close up of an orbital pattern and the right side shows a crosscut. You can easily see the two line patterns in the crosscut.
Keep in mind buffing compounds will remove sanding lines of 240/400 grit, depending on the type of abrasive used.