I'm not disputing glaciation had an effect, it's just that a decline in habitability of where the hominids were living was not an effect that can be pointed to as a cause of migration. If anything, there should be more outmigration from highly habitable areas than from less habitable ones. That's because any area quickly fills up to the limit of its carrying capacity, and the highly habitable area will then have more inhabitants to diffuse out.
The assertion is that change in environmental conditions allowed for migration:
They then pointed out that evidence in past research showed hominin habitation all across Eurasia started approximately 900,000 years ago, which coincides with the onset of the first Pleistocene ice age. As the ice age began, ocean levels would have dropped, allowing hominins an easier route from Africa.
Another assertion is that habitability had declined to the point where humans had almost become extinct:
Two recently published analyses make cases for severe bottlenecking of human populations occurring in the late Early Pleistocene, one case at about 0.9 Mya based on a genomic analysis of modern human populations and the low number of hominin sites of this age in Africa and the other at about 1.1 Mya based on an age inventory of sites of hominin presence in Eurasia.
A further assertion is that decline in habitability was specificly due to aridity:
We suggest that the best available data are consistent with the Galerian hypothesis expanded from Europe to Eurasia as a major migration pulse of fauna including hominins in the late Early Pleistocene as a consequence of the opening of land routes from Africa facilitated by a large sea level drop associated with the first major ice age of the Pleistocene and concurrent with widespread aridity across Africa that occurred during marine isotope stage 22 at ~0.9 Mya
It's your assertion that:
> a decline in habitability of where the hominids were living was not an effect that can be pointed to as a cause of migration.
and I can see no reason why you would make this claim.
I have already explained the logic behind the claim.
The things you quote there do not justify a claim that reduction in habitability would cause migration. They do justify a claim that an increase in habitability of nearby areas could cause migration to those areas. The hominids cannot diffuse into an area in which they cannot survive as a population (or rather, they can, but they just die out, so the spread stops), but if the area became sufficiently more habitable then those diffusing in could then sustain a population there and act as a base for further diffusion.
