Being equidistant from two south celestial poles, one should observe two points of rotation and stars converging upon each other when looking directly overhead, but one doesn't does one?
Can you provide any documented observations from a point equidistant between two south celestial poles to confirm this?
How far apart are these south celestial poles? Do they overlap? Are there empty regions between them?
That depends how many there are. There must be at least three - one for each major temperate landmass in the rimward annulus - and these could be expected to be found approximately 35 Mm apart. Further observation is required before conclusions can be drawn about stellar behaviour in the intermediate regions.
Unnecessary duplication? Without motive or reason?
The reason is that the stars are observed to be arranged as such. Of course, this suggests some cause for the similarity, but none has yet been found.
What if you could see a planet such as Jupiter, from Australia, where you could also see the south celestial pole, and then you went to Argentina and could also see Jupiter and the south celestial pole, and they would be in the same relative positions to each other - does that mean there are multiple Jupiters?
Planets follow the zodiac. They don't wander far enough south for this to become an issue.
If you were mid way between South Celestial Poles you would see stars next to each other that should not be.
As I asked Its a Sphere above, can you provide any documented observations which verify this?