I don't think that genetic diversity will necessarily slow under those conditions. Genetic differences between people are already dominated by individual genetic differences over group genetic differences. Our diversity is more about us as individuals than as a collection of groups. Why, then, would the mixing of groups decrease diversity? I would think it would increase it.
For example, Tibetan people have developed a genetic adaptation to high altitude. This can only have happened because of the relative isolation of that specific population. Now that we are constantly mixing and have technology to fix everything such adaptations are much more unlikely to arise or even to be kept.
All in all, the global human population will become more homogeneous and less diverse.
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I don't think that genetic diversity will necessarily slow under those conditions. Genetic differences between people are already dominated by individual genetic differences over group genetic differences. Our diversity is more about us as individuals than as a collection of groups. Why, then, would the mixing of groups decrease diversity? I would think it would increase it.
For example, Tibetan people have developed a genetic adaptation to high altitude. This can only have happened because of the relative isolation of that specific population. Now that we are constantly mixing and have technology to fix everything such adaptations are much more unlikely to arise or even to be kept.
All in all, the global human population will become more homogeneous and less diverse.
People being less adapted to specific environments is not the same thing as being less diverse.