ooh dear. To be fair, parts 2 and 3 would have been tough to adapt. The Swedish sequel knows it's nutty as a fruitcake and plays up to it, which I don't think Fincher could have captured. Meanwhile part 3 is a dull narrative with little to get stuck into. It's good and watchable, but I doubt it would have floated Finchers boat without an aggressive adaptation.
So, my first thought, long before he was lined up to remake it, when watching the original holds true. It's the best film Fincher never directed!