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The cost of annexing can be very high. War is hard on people, and we don't have methods of smoothly and sensibly rearranging national borders.
Also, at that point, country Y has inherited all of country X's problems.
As far as I can tell, you don't get everyone (or a very large proportion) of people wanting to leave a country unless there's a lot of violence or a natural disaster. If the problem is poverty, people would rather have some members of their families emigrate to work, and send money back.
I think "annexing country X" might show some problems with utilitarian thinking-- a tendency to abstract away important amounts of detail and the costs of getting from point A to point B. This doesn't mean utilitarian thinking is always wrong, but these are problems to watch out for.
That's my point. Having many people from country X emigrate to country Y causes country X to acquire country Y's problems.