> Others, you included, started on about war and migration
That's because the two are related - historic migration tended to accompany wars, because the "host societies" were not too accepting.
> so if you wanted to list what European invasion 'did' for Amerindians - comes out very negative on the whole. But the invasion worked out really quite well for Europe. Not a popular thought, but undeniable
Definitely undeniable, but the Europeans were the invaders, not the host society; so this is not a good example of "Migration has demonstrably contributed to the betterment of host societies", but the opposite ...