[J]ust as building a Death Star sent an important message to non-compliant planets, destroying a Death Star sent a powerful signal, as well. It was a huge public relations coup for the Rebellion. So the Death Star, while a devastating weapon, was also a tempting target. There were some basic conceptual design flaws (both versions were destroyed by a small smuggling ship and a handful of single-person fighters), but really, even if it had survived Yavin, it was doomed to spend much of its operational time fighting off attackers, simply by virtue of being such a big fat target.
Via The Daily Dish.