Yes, it was a Baysian not a mathematical argument.

I don't quite understand - Bayes is maths.

They are unless you have reason to believe the immigrants are above average.

One could require immigrants to have demonstrable skills. However, if the immigrants are above average then this causes a brain drain for the home country.

If most people from country X want to move to country Y then wouldn't it be easier for country Y to simply annex country X? You save on relocation costs and the people are now in country Y.

This would also stop smaller first world countries like the Japan or the UK becoming overcrowded. OTOH its also completely infeasible in the foreseeable future because people wouldn't agree to it.