Given the length of the access routes to the chambers in the G.P. isn't it unlikely that any 'robbers' official or otherwise would have removed even the sarcophagus lid and a fragment of the sarcophagus along with all the grave goods.
I accept that Kufu built the pyramid, and I think that perhaps he and his accoutrements were removed to another location, possibly hundreds of years later, and being pragmatic that later state may have decided to recycle any valuable goods rather than intern them for a second time - but there should be some trace in those tortuous passages.
Where is the sarcophagus lid?, I met a Professor at Oxford who was adamant it went down with a ship in the med. back in victorian times, but I don't remember much more than that.
IMHO, the missing sarcophagus lid isn't that hard to explain, like many tombs the GP wasn't only visited by tomb robbers but also by stone robbers. Some of the granite porticulis blocks that sealed the KC from the Great Gallery have been found outside the pyramid, the lid was also removed and probably re-used or recarved for other purposes (or smashed when the pyramid was robbed). Same with many granite casing stones from Khafre's pyramid.
Given the fact that of all pyramids the GP is/was the most famous and attracted the most attention both in ancient and modern times, it isn't all that surprising that it was totally emptied.
The ship that sunk in the med. back in victorian times had the sarcophagus of Menkaure on board.