As we know, Abstergo has at least 4 Apples. #1 (Stolen from Houdini) #2 (From Gandhi) #3 (From Kennedy) and #5 (From the Moon). Abstergo needed an Apple to finish the Eye-Abstergo project after Daniel Cross destroyed Apple #2, and that's the reason why they kidnapped Desmond and Clay (To find Ezio's Apple). But... why didn't they use the other Apples?
Yeah, that's what Darby MAYBE implied on one of his usual jokes to a serious question. "Ezio's apple was a red delicious. The others were a granny smith, a braeburn, a honey crisp, and a fuji, in that order."
Using Precursor artifacts like the Apple required Precursor genes. Desmond had those genes. Maybe that's the reason they kidnapped Desmond and could'nt use the other Apples. Also, Subject 16 and Desmond both had Ezio as their ancestors.