I think Theo signs FA's in an attempt to keep up with the Yankees and not to respond to the demands of the fans. As much as I would like to think that he responded to my daily memos asking him to sign Crawford, I don't think that was the deciding factor.
As far as FA's that have done pretty well in recent years, off the top of my head I would say Sabathia, Damon (twice - once for the Sox and once for the Yanks), Holliday, Beltran (3 very good years out of 5), Hideki Matsui. I am sure that there are others. I very much wanted Holliday in 2010, but he took a pass.