Ok and people are blank pages without cultures or tendencies, which means we can just graft them without issues?
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.
You need integration initiatives and strong enforcement. Integration is a two-party process, if either side doesn't take it seriously, it won't happen. We should be generous in giving out chances, but strict in taking them away from people that prove they're not making use of them.
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.