This topic came up on a local Kansas City sports talk show this week while discussing The Masters, Augusta National, local players and their experiences, etc.
One of the hosts suggested that Augusta National host a Ryder Cup and thought the Club would jump at it if approached. After a long period of time of talking about how cool of an event it would be, especially seeing best ball matches and head-to-head match play, calmer heads prevailed.
It ended up the rational ones didn't think the Club would go for it for a lot of reasons, mainly, it is still a very PRIVATE CLUB. It was also felt the boorish behaviour during the Ryder Cup would be difficult to control since it brings in a different crowd than the Masters and 'National' has no control over who gets a ticket. Also, the Ryder Cup is played in September, long after the azeleas have bloomed and maybe the course doesn't show quite as beautifully.
It is a discussion worthy topic.
I'd love to see it happen though and I'd volunteer to help with crowd control.