The real issue is that the integration process is actually slowed as the level of un-integrated immigrant increases.
The inflow has to be matched by the outflow (the integration capacity) to have a sustainable immigration policy.
The West in its ideologically enforced multiculturalism phase has had and is having unsustainable immigration levels well exceeding any host societies capacity to integrate. To make matter worst there is one more effect and the left-wing fascist greenies love using the notion: the tipping point. The capacity to integration not only slows as the pool of un-integrated immigrants and their descendants increases, but it also reaches a tipping point where long terms parallel societies are formed out of these ghettos that out friend above romanticises about. It is this development of parallel societies open to political guidance for foreign colonial powers (eg Erdogan or Turkish diplomats in Vienna) that we are seeing today.