The entire EU is dying out slowly from low birth rates. Our only hope is replenishing our population through immigration and anyone that argues against that is arguing against the survival of Europe.
This is without all the social issues of putting them in ghettos and pulling up the ladders to their kids to integrate in society.
It works like debt, in the sense that you are taking a band-aid solution and kicking the can 15 years but they have been doing it since the 1980s so the can is here now.
There is also a dilution process by which you assimilate or adapt a population and if the % of new people is too high the culture that produced those societies basically disappears.
The last argument is empirically incorrect. Think of Vienna for example, most of the population there has roots from all over the Austrian Empire. Yet, it's distinctly Austrian.
It's not a given, it takes effort. But it can be done.
Population cannot grow forever, and for the sake of the planet it may even good if it dropped. So this is something that we'll have to face at one point and the argument that there is not choice but mass immigration is a fallacy pushed to silence dissenting opinions (along with labelling dissenters racist and far-right).