it's better than paying for natal care and education for a local-born child who will still have a high carbon footprint, and might also not be as productive as the immigrant

And one could argue that: 1. Immigrants typically have higher TFRs that within years wipes out the gains you allude to 2. Productivity depends on how skilled the immigrants are; much of Europe has a large chunk of immigrants with lower productivity than the native born. Anyway, this is a low signal discussion on both sides; this is my last comment on this matter