The decision to scrap and rewrite is a case-by-case call. Sometimes the design is so flawed, outdated or shortsighted that scrap-and-rewrite is clearly the best option. Sometimes scrapping just one or a few layers or modules will achieve the desired effect.
I've seen two extremes in one project (Macavl, he says as he waves to Bruce Cook, Major and the ghost of Dean Elsner), one where the boss refused to rewrite the original program until the overlay tree became so banyan that it broke STB ("Slow Task Breaker", although the official DEC acronym was different) completely and left him with no choice, followed a little later by a period in which the wheel was repeatedly reinvented in slightly different ways because it wasn't quite right.
Implying as Chromatic does here that rewrites are always superfluous is wrong, as would be the person who constantly rewrote the program, striving for perfection Zeno's-tortoise style until all of their followers make the Achilles decision. Let common sense prevail!