Returning to the topic of the original post, apart from the long term political, moral and ethical considerations of migration, there are more immediate logistical problems to consider.
The main problem will be economic and social integration. European Union is broken. Economy never recovered to 2008 level. Almost all countries operates below the economic peak achieved prior recession. There is not only Greek economic collapse, but even fast growing economies are still underperforming. There is not enough jobs for educated Europeans, and now you deal with people from Yemen, Syria, Eritrea, who are 20% to 40% illiterate. Very a few will be able to integrate in European economy and will live off welfare until the welfare system collapses. Government cannot rise significant taxes without facing widespread opposition from its public.
Once refugees will realize that they will not get 2000 freebies monthly and they will live in poverty with the rest of Europeans, they will riot. Without significant improvement in economy, EU will cave in under this immigration invasion. This is already happening in Sweden and Germany where social nest, housing, welfare are already strained. Netherlands and Sweden already singled out Visegrad 4 for their internal economic problems.
So, the outcome of this multicultural social engineering will make every European poor. Democratic principles are already undermined by silencing opposition to immigration. We are witnessing disintegration of Schengen agreement. What will Europeans do when their find in their economies fragmented and localized, while living through 1970's income and choice of goods?