I'm Australian, have lived in the US, and now live in Denmark. I'm also pro immigration, both for skilled and unskilled workers. However Non-Western (as defined by the Danish Ministry of Statistics) has been financially costly for the welfare state, and the assumption that unskilled immigrant descendents will (as a whole) outperform their parents has not been realized.
There's blame on both sides. Denmark doesn't do a stellar job of integrating outsiders despite ample funding. Likewise there are cultural incompatibilities, such as the handshake-citizenship debacle in a country that has arguably the closest gender equality in the world.
My personal lesson is that immigration is really complicated. I truly believe people should be free to move wherever to realise their maximum potential. But in holding this standpoint you must acknowledge the very real costs incurred.