I asked a similar question last year but didn't get any answers. It seems from just Wikipedia, that a lot of Bronze Age cultures had palace economies, which seem to me to require some pretty extensive bureaucracy and control of the population. Yet, Palace economies disappear after the Bronze Age, right? And the the empires that replace them don't seem to regulate production and distribution of stuff anywhere near as heavily. So how exactly did the Bronze Age states manage this where later states didn't?
I'm not an expert in this area, but there are a couple of points that perhaps need clarification.
And I don't think that you can call these misnomered Mycenaean states an 'empire', anyways. Furthermore, although it's true that Hattusa seems to have been destroyed during the Collapse period, Neo-Hittite states persisted quite well until the Neo-Assyrian Empire developed a true hegemony in the area, and Egypt, of course, didn't suffer anything like the damage that Greece, central Anatolia and the Levant did.
I don't want to downplay the setback that Mainland Greek States suffered - clearly, it took 250 to 300 years for populations, trade and politics to recover. But the 'Dark Ages' were not universal to the whole of the Eastern Mediterranean suring LBA/Iron Age transition period.
Perhaps if you clarified what exactly you mean by 'Palace Economies', which ones and for what time period you are referring to, and which less-developed Empires you are referring to that supposedly replaced them less successfully, someone with more knowledge might be able to help you.