To make the impact of a change request more tangible, I suggest using an example most of us can relate to - home renovations. Last fall, I had a series of basement renovations performed. One component was to add a partial wall to split an area of a room off (notice the wall on left.)
Had I realized my requirement for a longer dividing wall earlier, it may have saved my contractor some time (because I caught this early I didn't waste any materials.)
For arguments sake, suppose I figured out I needed the wall extended after all the painting, floors and baseboards had been installed. Considerably more time and material cost would have been incurred. Why?
If my contractor needed to remove flooring, drywall and repaint - I would have wasted a lot of materials. Some of the flooring and baseboards would have been thrown out, additional paint and priming time would have been required, etc... All of this costs money.
On a side note, the wife of a friend of mine was also performing a renovation - the kitchen. She decided to replace the marble tile pattern she had picked for the backsplash. She made this decision after the tiles had been bonded to the walls, grouted and treated (so oil wouldn't damage them.) My friend literally cried... he understood the impact.
The moral of the story - the earlier you can identify the need for a change the less costly it will be.