Common sense was that Ocitanians and Bretons could never integrate into France.
Common sense was that hundreds of independent principalities with mutually unintelligible languages could never integrate into Germany and Italy.
Common sense was that Samnium and Lucanium could never integrate into Rome.
Except all of them did and those countries were stronger for it.
That's the belief. The reality is that the onus is not accepted and largely does not resolve for a couple generations. In the short term, the effect is obvious. Pure disruption from an economical and cultural perspective. A melting pot of the worst and best of both worlds. The worst effects necessarily dwarfing the short term benefits.
However, in the long term, a melting pot/diversity is believed to always be a net benefit. I'm not sure why the belief persists, other than convenience (can't really unmix populations after generations) and confirmation bias. Economies improve over time or nation economic models disappear, making it moot. I believe how a nation specifically deals with immigration has influenced the outcomes a great deal, for the better. Not dealing with immigration as a serious, ongoing concern, is a crap shoot.