Mass immigration works as long as policies are in place to enforce assimilation and integration into the existing melting pot, rather than this failed multikulturism b.s.
When integration fails, at least 50% of the blame can be attributed to those in the native population who were hesitant to lay down the ground rules and push for assimilation from the start. They are scared that it would hurt their "progressive" cred, and so they chose to stick their heads in the sands instead when they sees things that are clearly incompatible with Western values, until it's too late.
The tragedy at Rotherham and Cologne are a prime example of this egregious mistake. When someone migrates to a new land, the very first thing that should be drilled into their head immediaty is that they are expected to bring the best part of their culture while leaving the worst uncivilized bits behind, or be deported. If the new arrivals think they can just act like how they were used to in the whatever third-world shithole that they escaped from with impunity, then their new adopted homeland is in a world of trouble.
I think the U.S has been doing a very good job at maintaining our melting pot in the last 200 years, where everyone rallies under the American flag and stride for the American Dream, no matter where they came from. Our robust but orderly immigration process brings in over one million new immigrants from all over the globes each and every year, and their successful integration have contributed greatly to our society.
Mass immigration require two things to work: the new arrivals are willing to integrate, and the government making it abundantly clear from the start that assimilation is not optional.