I think I remember some clockwork ones that had auto stop, but I could well be wrong.
Did a search and Beachcomber I think you may have it right.
I saw one comment that all 78’s originally had concentric run outs but it was found that a steel needle left running in the groove could carve a hole in the record so the eccentric groove was developed, not sure I buy that.
There does appear to be a common view that it was designed to activate auto lifts on electric powered 78 players and early 33/45 vinyl. Early auto lifts were according to some comments triggered by velocity hence the sweeping inward motion.
Apparently an RIAA standard that was revised to a concentric groove with the advent of early stereo records around 1958/59.
No idea if any of the above is fact, but sounds plausible.
Interesting though, now where did I put my anorak!