After a bit of staring at maps and head-scratching, I conclude that you must mean the missing chord at Staverton.
Actually I wonder what purpose the chord at Thingley served - though given that it was opened during the war and closed before 1960, I presume it had something to do with munitions and the various facilities buried round Box.
There was a major freight depot / yard at Lacock, just to the south of Thingley, and freight from there feeding into the MOD areas around Box tunnel. The chord also allowed freight from that yard to have a good route in from and out to the Bristol area.
Restoring the chord at Bradford Junction was in the Network Rail electrification proposals at one stage, just as the extra platform line at Westbury was in the Reading program. Both would have been potentially beneficial spinoffs of their programs, and undoubtedly would have / will help as works happen. However, both were "nice to do" options and were naturally removable as the projects were pared down. The cynic may wonder if they were initially included, indeed, to allow negotiating space.
Looking ahead to either curve being re-instated in the future, I have to admit to being of two minds. I can see use for both / either of them, but I can also see a danger in that if local passenger services on the TransWilts were split to go two ways at one end of the line or the other, we could end up with two services both with a frequency below the minimum needed to attract general growth.