Cukor was one of the greatest directors of Hollywood's Golden Age and continued to make quality films until he retired in '81. His last two films, The Corn Is Green (TV version) and Rich and Famous are both quite good. However, My Fair Lady is not Cukor at his best. He probably was not the ideal choice for a film version of a classic book musical. Vincente Minnelli would have been better suited for the material.
The My Fair Lady film has a lot of flaws. However, it still holds up has a solid, entertaining film version of a great stage musical. I would categorize A Chorus Line as a misguided film version of an excellent stage musical, badly directed by someone who knew nothing about the genre -- a disappointing film but watchable for non-discriminating viewers. The Mame film is god awful, a disaster, and completely unwatchable (for me, anyway).