Traditions of groups-
If "Georgia Sea Island Singers" is an organized group singing Sea Island songs, they would have the right to copyright their arrangements of their traditional music.
If the singers get together informally and sing traditional songs of the Sea Islands, there would be no issue of copyright.

The "Northern Neck Chantey Singers," retired menhaden fishermen, are able to copyright their arrangements. An informal group, however, would not have that privilege.

A similar situation exists in the case of old cowboy songs.
Mark Gardner has issued a volume* containing some of Jack Thorp's "Songs of the Cowboys," including some from Thorp's little book of 1908 (copyright N. Howard Thorp) and his later book (1920's). The new book includes a CD made with Rex Rideout. New material and arrangements are copyright.
The statement in the book reads- "Copyright © 2005 Palace of the Governors. New text © Mark L. Gardner. Illustrations © Ronald Kil. CD recording © Palace of the Governors, Museum of New Mexico. ALL RIGHTS RESERVED. No part of this book may be reproduced in any form or by any means whatsoever without the expressed writen consent of the publisher. Museum of New Mexico Press is a division of the New Mexico Department of Cultural Affairs."

To me, that is perfectly fair in that it protects the rights of the participants to income from their production. In this regard, I see nothing wrong with current copyright regulations.
Anyone is free to sing the 'traditional' songs, and those by known composers, if copyright has expired, providing that the work and arrangements of the participants in the book and CD production are not infringed.

*Edit. Mark L. Gardner, 2005, "Jack Thorp's Songs of the Cowboys," 89 pages and CD, Museum of New Mexico Press, Santa Fe.