>Humans aren’t particularly genetically diverse, given our dispersal, though as far as I know there’s some disagreement on _why_.

That's absolutely correct. One set of hypotheses about this are population bottleneck theories[0].

As an example, the Toba Catastrophe Theory[1] posits that:

"The Youngest Toba eruption has been linked to a genetic bottleneck in human evolution about 70,000 years ago,[28][29] which may have resulted from a severe reduction in the size of the total human population due to the effects of the eruption on the global climate.[30] According to the genetic bottleneck theory, between 50,000 and 100,000 years ago, human populations sharply decreased to 3,000–10,000 surviving individuals.[31][32] It is supported by some genetic evidence suggesting that today's humans are descended from a very small population of between 1,000 and 10,000 breeding pairs that existed about 70,000 years ago.[33][34]"

Whether such theories are correct or not, they appear to fit with the lack of genetic diversity among humans.

[0] https://en.wikipedia.org/wiki/Population_bottleneck

[1] https://en.wikipedia.org/wiki/Toba_catastrophe_theory#Geneti...

I'd have assumed that it's largely because humans can spread to new niches via cultural evolution, which happens vastly faster than the old-fashioned biological kind. Much quicker to make a fur coat than evolve one.