Of course, that almost never flies in the business world. They'll ask you why on Earth the company should pay to build something again before they make money from it. However, it truly is a powerful engineering process for many types of problems.
The point is not to merely rebuild it for arbitrary reasons. Rather, to take stock of the benefits and the pain that arises from the current design, and to try completely different approaches. You do it because there's a nagging voice in the back of your head that tells you that you've left some "goodness" on the table ... that even though your current implementation "works", the problem could be solved better.
You've already "loaded the problem into your head," because you've solved it once. The second solution will improve in some ways and possibly regress in some ways. Often, the 3rd or 4th solution will be "right" -- which means, not perfect, but significantly better than your earlier approaches.
It seems kind of like learning the card game of Bridge by playing the same hand over and over to see if you can get it better. Or learning chess by starting from the same canned starting position and seeing if you can play it to completion better.