Your "extremely likely" scenario is the "cold winter theory", which is problematic for many reasons including the myriad of historical instances where hot-climate civilizations outpaced cold-climate civilizations.
How would you explain how geographically distant groups in radically different conditions could, over millennia, converge on all of the exact same non-visible traits without even minor variations? I truly can't imagine a way that this would be possible aside from the infinitesimally unlikely product of completely random chance.
You're not even telling a coherent story at this point. The "cold winter theory" isn't merely that the populations are different (though: again: when you look at the molecular evidence and the way genes propagate, it's nowhere nearly as clear as you'd think), it's that the cold winter populations are smarter. But you have to literally ignore most of human history to reach that conclusion. Somehow, in this view of the world, evolution only kicked in a couple hundred years ago. Seems unlikely!
How would you explain how geographically distant groups in radically different conditions could, over millennia, converge on all of the exact same non-visible traits without even minor variations? I truly can't imagine a way that this would be possible aside from the infinitesimally unlikely product of completely random chance.