A lot of the modern ideas of immigration arent so much truisms earlier in history.
The regions surrounding the Steppes suffered regular depopulations followed by mass immigration from multiple peoples repopulating those areas. Urgench went from being sacked for instance to being noted for just how populous it was (untill Timur of course). The resistence to immigration and absorption of immigrant populations is a side effect of nationalism, which may be averted given the right POD.
Welcoming in migrants to repopulate an area is a little different though - here, were are talking about a Europe that is already very crowded (much more than OTL) so I'm doubtful that mass immigration would be welcomed.