It is incorrect to state that Persian records are sparse - there are tens of thousands of tablets from Persepolis, primarily from the reign of Dareios to that of Artaxerxes I (So into the 450's BC). However these mainly detail mundane matters of logistics - grain, wine, construction crews, etc. While immensely valuable to historians laypeople tend to be bored by this kind of information and so it has little popular currency.

On balance it seems likely that there are more stashes waiting to be discovered - unfortunately many of the urban areas of Iran have been continuously inhabited since Achaemenid times, so it's not just a matter of taking an excavation crew and digging until you find something. It-?'s a contentious matter to this day.

As for why there are no literary histories - if they existed, they were not copied. It seems likely to me however that oral epic would have been the preferred medium of the Achaemenids, and faint traces of their history (like epithets of kings known from Greek sources) can still be found in the national epic of Iran, the monumental Šah Namah ("Book of Kings"), in turn based on a lost Middle Persian predecessor, the Xwaday Namag ("Book of Sovereigns").