Unless there was an original purpose that was taken out, there does indeed seem to be a lack of purpose. From what I can tell, the crimson loftwing was meant to do a couple of specific things that may not be easy for people to spot. The first purpose was to link the red bird on the Hylian shield to a specific purpose. There has been alot of speculation as to what this exactly means. By specifically giving Link and only Link a red loftwing, it's easier for the player to connect the traditional shield to the original hero. If just anyone could have a red bird, you could still connect it to Link, but this situation makes it that much easier. Another reason is more recognition that Link is special. Notice how Groose says "and I don't care how tough those bird are supposed to be." This is a sign that not only is Link's bird special in rarity, but also in endurance. Apparently Link and his bird also share a connection more deep than most people in Skyloft have with their bird. Pretty much everything about this particular loftwing is special. By gaining this rare bird, it is a continuing demonstration that Link is not only the hero of the story, but a chosen hero. Like that one guy from Clash of the Titans, his journey is made easier by gifts. Though I have no direct proof that Hylia gave Link his loftwing, this sentence by Gaebora is very convincing. "[...]loftwings, the guardian birds that the goddess bestows upon each of us as a symbol of her divine protection."
So while Link having a crimson loftwing did not serve a purpose specifically to the plot, it was a symbol of other literature means. I do believe, though, that an addition to the plot would've helped enhanced SS's story a great deal.