Having Father Christmas also drives home an important point. What Jesus did on earth is to be universally celebrated in all of God’s Creation. The gifts of Father Christmas were not trivial; they were what were needed for to accomplish what was prophesized.
The Narnias must have had a knowledge of what Jesus (Asland) had done in the home lands of Adam and Eve. If I had to guess, Christmas was an integral part of Narnia since its creation (brought there by Queen Helen and King Frank in “The Magician’s Nephew”). Lewis also stressed that man made religions which existed prior to Christ coming were man’s attempt (although somewhat warped) to reach out to God and they had some truth in them. He incorporated this theme in both the “Chronicles of Narnia” and his space trilogy. He rejects religions which came after the Incarnation as see in “The Horse and His Boy” and “The Last Battle”. “Tash” is not “Aslan” and Allah is never to be confused with the Judo/Christian understanding of who God is.
You make good points...it's just that with Father Christmas appearing as Santa it makes it rather hard to take that part of the movie seriously, when, as you point out, it is instead supposed to be a moment of great import and not trivial at all (the silliness of the situation was further emphasized with Mr. Beaver saying "i hope you've all been good" and then later Lucy quipping "see, i told you [that he was real]").
By the way, could the gifts be seen as somewhat analogous to the gifts of the Wise Men? I can't remember if Edmund was with them then or not. I'm pretty sure though that he wasn't and therefore only three gifts were given out, just as when Jesus was born.