I was just on holiday in south eastern Europe in a resort town where the workforce was entirely composed of the same kind of immigrants, and none of these immigrants were "integrated" by this standard. But there was no criminality. Maybe because all of them were gainfully employed and felt like they had a future.
That's just one example.
My point is, there is a false equivalence being exercised here. Just because somebody is not integrated by whatever arbitrary standard, does not mean that they are prone to engage in criminal activity.
If you don't integrate and don't learn the language and never have any contacts outside your community, how are are you supposed to survive, find a job, find spouse and eventually move out from those neighborhoods?
So you either live on welfare or you turn to criminal activities. What else is there?
In which world do you live where not knowing the language is ok for any kind of job?
If you can't understand your coworkers communicate with your managers, talk with you colleagues, how are you supposed to do your job properly then?
It is perfectly reasonable to expect that if someone moves to a new country, they should learn to speak the language so that they can be understood and be an active participant in said country.
If this person is not willing to put in this kind of work, then that is not acceptable. You can't expect the local population to do the work for the immigrants. And that criteria applies to western immigrants too.