Based on your argument though, the sensible way to do it would be to offer asylum predicated on some kind of IQ test to ensure that we’re getting all the Caucher Bitkars our there and not wasting too many resources on lesser intellects.

Indeed, what would really make sense is for developed countries to be actively working to apply IQ tests to every third-world shanty town out there, and actively paying high-scoring individuals to immigrate.

In the real world this kind of thing is generally considered somehow to be in bad taste, so most developed countries go about it in a rather more roundabout way. Still, any country which actively started recruiting would find themselves with a huge advantage (at least when it comes to Fields Medals).