My reason for immigrating is simple: in a developed country I'll make more of a difference with the same amount of effort. My "hash" inclines me to move to developed buckets (and also privileges me with the means to do so). Take Elon Musk as an example. If he attempted to start SpaceX in South Africa (his country of birth) he would have been hemorrhaging capital via the corrupt government tender process. There is also the added problem of a lacking employee pool due to the on-going brain-drain. His "hash" landed him in a developed country and is demonstrably an advantage because of many factors, including the support of the American government.
I really don't think that immigration changes people; it's merely a tool that the inspired use to achieve their goals. The anthropic principle could be invoked here in a contrived way.