This is factually not true, and you can easily see it in the correlation between waves of immigrants and the crime rates going immediately up. We aren't talking about just organized crime, but also petty crime, rape, etc.
Usually, after 2 generations, most people adopt the local culture. You can see it in quite tangible metrics, like, for example, they stop having many children, with the fertility rate dropping to the Western average. And if first and second generation descendants become a problem, indeed, then we can talk about society being broken, and the solution is to fix it, not to stop immigration.
For me, talking about slowing down immigration is like talking about slowing down the economy. It can't be done without people eventually starving.
Usually, after 2 generations, most people adopt the local culture. You can see it in quite tangible metrics, like, for example, they stop having many children, with the fertility rate dropping to the Western average. And if first and second generation descendants become a problem, indeed, then we can talk about society being broken, and the solution is to fix it, not to stop immigration.
For me, talking about slowing down immigration is like talking about slowing down the economy. It can't be done without people eventually starving.