Getting immigrants who work is a non-issue. I never heard of immigrants from India, China, Africa or Latin America who don't work so long as they entered the country legally. The issue you are alluding to has to do with genuine refugees and illegal economic migrants, who are not filtered at the border depending on their employability within the local market.
But the cultural shift is still inevitable. A foreigner is not a local, and it is neither fair nor ethical to expect a foreigner to transform themselves into a local.
I think, if you are concerned with the cultural shift, you can give immigrants temporary term VISAs and make it clear their stay is going to be strictly temporary. That was supposed to be how the Gastarbeiter system works. Thing is, when you have already on boarded a foreign worker and have had them working for you for 2 years already, you don't want to let them go and replace them with a fresh foreign worker who you have to retrain.
I think, if you are concerned with the cultural shift, you can give immigrants temporary term VISAs and make it clear their stay is going to be strictly temporary. That was supposed to be how the Gastarbeiter system works. Thing is, when you have already on boarded a foreign worker and have had them working for you for 2 years already, you don't want to let them go and replace them with a fresh foreign worker who you have to retrain.