That's an unsupported assertion.

Lots of non-Ukranian Europeans still want to move to the US for example, because there's an idea that in skilled jobs you can make more money in the US.

Likewise, India isn't "kept" in poverty nor is the country at war, but the opportunity for economic prosperity elsewhere is a strong driver for migration. And when India surpasses the US or Europe in economic prospects, the trend will reverse and enterprising people will flock to e.g. Hyderabad and New Delhi.

Economic prosperity, until we do away with capitalism, probably won't ever be homogeneous. Where there's a potential across a circuit the electrons will flow.