There never was a scriptural basis for it. SV:
if I remeber right, the changing of the chairmanship between Peter and James in the first century GB*** discussion on the circumcision / blood question, that happened during prolonged interruptions prompted that.
That was the then very convincing scriptural argument at the time, and allowed the manipulators to rotate a willing victim into the top job for the 1975 fiasco ; ha ha.
In the context of today's watchtower it would have given a good lesson of getting all brothers exposure, experience to the different tasks, and relief from the stagnation that preceded that rotation too, when congregation servants were on the top for life.
*** The only reference for "organisational" procedure inside a "body" I know of in the NT. bsw.