It is more of a "long term experience" than mere "assumption".
At least in Europe, a sizeable amount of illegal migrants has only very rudimentary education, and the # of job openings for unqualified people is very limited. Some literally cannot read even in their own language.
As a result, immigrants from Africa and the Middle East are, on average, significantly overrepresented among welfare collectors and significantly underrepresented among taxpayers.
Of course, as long as the numbers involved are tiny, you can try to educate at least their kids, but once a fairly low threshold is crossed, parallel societies develop in full. Having classrooms where 90 per cent of the kids don't even speak the official language of the country is quite an intractable problem. And that threshold beyond which the schooling system basically gives up has been crossed in many regions of many countries such as Sweden or France.
TL;DR: You cannot maintain a modern welfare state with premodern population.
