I didn't watch the first two seasons live, so the first Tennant episode I saw was The Girl in the Fireplace. Given this, the Christmas episode to me wasn't "when will I finally see the Doctor?" it was "The Doctor needs to recover to save the day." Given that, his absence added to the drama (which otherwise would have been completely missing in an episode that wasn't overly exciting). I realize that, for those who were watching it as their introduction to Tennant, it falls a bit flat. However, his absence, to me, fit the story rather than detracted from the story.