If every country had open borders then in a few generations every country would be essentially culturally identical (and English-speaking), massively reducing the cultural diversity and vibrancy of the human race as a whole.

I doubt "vibrancy" would be lower. And there are major cultural differences within countries, including countries that have existed for a very long time. I agree that cultures would merge more, but that is not a bad thing. The same thing is going to happen over a longer time scale with closed borders anyway.