You're ignoring the WhatsApp factor. Immigrants experience first hand how well Western democracy works and then share that with everybody back home.
It's also quite common, at least in my experience, for people to follow politics back home. Invariably, they advocate quite vocally for more democracy, less corruption and less discrimination.
Don't forget that many developing countries have a wide array of policies in place to ensure that they can't make proper use of their human capital.
My father-in-law, for example, is an environmental scientist who simply couldn't find work in his field (public sector) back in South Africa in the early 00s as there were racial quotas and affirmative action policies that didn't work in his favour.
He was offered a job in NZ, after a solid year of being unemployed, and jumped ship immediately. His talent wasn't stolen by the developed world so much as it wasted by his underdeveloped home.
We are saying the same thing.