If you took two different training sets then it would be more surprising.
Or am I misunderstanding what you mean?
If the populations are different, then you'll just get two models that have representations of the two different populations. For example, if you trained a model on a sample of all old people and separately on a sample of all young people, obviously those would not be expected to converge, because they're not drawing from the same population.
But that experiment of splitting one training set in half does tell you something: the model is building some sort of representation of the underlying distribution, not just overfitting and spitting out chunks of copy-pasted faces stitched together.
If there's some fundamental limit of what type of intelligence the current breed of LLMs can extract from language, at some point it doesn't matter how good or expansive the content of the training set is. Maybe we are finally starting to hit an architectural limit at this point.