The bracers do keep his shirt sleeve out of his string, which is important, because the tiniest snag on release can send the arrow dangerously out of control. ...Long hair causes the same problem, and it can be eliminated by braiding the hair tightly against the sides of the head, especially around the ears. Therefore those little elf-braids are not mere decoration; they are functional.
And on the second quiver he gets, from Lorien... (I didn't even notice he got a new quiver. I didn't notice the new bow either until the extended edition, when the gift-giving is actually shown):
The second quiver is carefully-shaped leather, embossed and gilded with a peacock design. Perhaps a comment on the Fellowship's most decorative member?
Thanks much to pegkerr for finding and posting this.