"Nobody 10,000 years ago had blue eyes,"

My reaction is that he misspoke here or he overstated his claim to make a point.

I know nothing about the proportion of people with blue eyes back then or right now for that matter. But I think at the very least, you could only make that claim with a tiny, tiny, tiny amount of confidence.

Maybe the proportion of humans with blue eyes was smaller back then, maybe it was larger, or maybe it was the same. I don't know. But to claim nobody 10,000 years ago had blue eyes is an impossible point to prove unless you have DNA samples from every human alive 10,000 years ago. We might be able to say that all the people alive today with blue eyes descended from one ancestor, but we can't claim to know about the population of people with blue eyes back then. For all I know, half the population 10,000 years ago could have had blue eyes but then got wiped out by swine blue.

That's like saying no one 100 years ago was over 7'6" tall. I know a bit more about height and think that this statement may be true. But it would be real hard to prove. Now shift the timespan back by 2 orders of magnitude, and I think it'd be harder to prove.

I'm not saying that the general idea is wrong, but I'm just it would be a good idea to question that claim a lot before thinking about reasons why that might be the case.