Plenty of movies I agree should be listed have already been listed, leaving me with just this to say about that:
I’d argue that Sweet Bird Of Youth, considered on its own, is a terrific enough film for you to see why it racked up award nominations for the lead actor and the lead actress and the supporting actor and the supporting actress — unless you start playing the Might Have Been game by comparing it to the Broadway version that so many of the castmembers were in beforehand.