As a result, what we're treated to is "Julie Andrews in musicals she would have been great in on Broadway, but never performed on stage." As in this case, her playing 'Anna' from The King and I, singing "Shall We Dance?" with -- Mr. Snufalufagus.
(She did record a studio cast album of the show with Ben Kingsley as The King. And it's very good. Though it's just audio, of course, and he's no Mr. Snuffaluffigus...)