"One example that worked: The original TAT (AAT in other lands) had turn areas described by radials and arcs from a point. We stayed with the simpler circle and they finally came along."

Sorry, no. Radials and arcs (more often called 'wedges') are still in the FAI rules (Annex A, 7.5.2b) and actively used in other countries.
Popular in Australia at the moment as a timesoak as when set 'pointing' at the finish it brings all the gliders in on the same heading.