the creature explodes in so many pieces

The lead beneath was still hot and a viscous liquid. The pieces would have fallen into that. Since the only witness left doesn't appear entirely sane, let alone willing to cooperate, it's quite possible they never even learn the exact fate of the original alien, assuming they even learn of its existence at all. All we know for a fact is that they know Ripley had a Queen inside her. Indeed, the way they enter the facility, with medical and biology staff predominant and armed guards sort of just tagging along suggests they didn't know there was a deadly full-grown xenomorph running loose.

Besides, if it were that easy, they wouldn't have had to sacrifice so many people to bring back an intact egg or embryo. Just shoot a piece of one off and pocket it. Burke wouldn't have had to go through his elaborate plan if all he needed was a fragment to bring back. Apparently, cloning technology has its limits in the Alien universe.