Life for me is about more important matters - family, friends, my own happiness going back to everything. And yes eventually world will over-mingle, the only way this won't happen is some proper catastrophe that will return whole humanity, or tiny remainder of it back to caves.
You want benefits of travel trivially globally but forbid people falling in love elsewhere and making kids, moving for better life or simply location/climate/culture they feel is much better for them?
In 1000 years most if not all countries we know now will not exist, maybe even memories and records of it will be vague and incorrect. Thats the lens I use to judge what is worthy of an effort and what is not.