I suspect, but don't really know for sure, that in the "old days" the big end of a tapered rod was the end that pushed the ball down the bore. And when I use an iron tip on the small end, I generally put a brass band at the big end, like on RCA 42, which is probably there to prevent splitting. Inside the band the wood is concaved to center on the ball.
If I use a modern 5/16" brass tip, I do nothing to the big end. In this case I use the small end for pushing the ball. Modern tips are concaved for this purpose, and work well.
Hope this helps,
Andy