Part III was all right, not as good as I and II, of course, and not nearly as good as it could/should have been, but it was all right and had some intriguing story points.

It is unfairly trashed because it wasn't as good as its predecessors, which were only probably two of the top 20 American films ever made.

I don't see any reason a GF IV couldnt' be made, and made well, if there was really a committment to make it a fitting installment in the series.

Puzo being dead isn't a deal-stopper to me - any GF IV would certainly make heavy use of plot points contained in Puzo's GF IV concepts.