The problem I see is that by invoking heritage/past, there's the thorny issue of Europe's sordid history of going to other cultures and exploiting them. Perhaps this gives 'us' even more responsibility to accept people into our culture.

I don't necessarily agree with that logic myself, but then I also don't feel that I'm entitled to what my 'heritage' brought me.

Personally my main concern with this whole issue is practicality. I'm concerned that a too-large influx of refugees (or economic migrants) might cause severe destabilization and further increase the growing right-wing sentiment.