FFC at the time of GF filming was a promising but relatively unknown director. Even he admits that one of the reasons he was selected to direct it was that Paramount figured he'd bring it in under budget, and he was under tremendous pressure to do so. It took plenty of chutzpah for this new kid on the block to convince Paramount that they could make money on a film that ran almost three hours. So it's understandable (but regrettable) that many fine scenes didn't make the final cut. By GFII, Coppola had almost total artistic control, which is probably why fewer scenes were deleted from the final cut.
I agree about the Genco scene. But then, all of the deleted scenes are gems--every one of them.