I think most of us agree that migrants traveling long and dangerous distances to Europe don't have much to loose back home. Now the question is if their lives are not in danger anymore why should Europe host them and pay them a better life ? Is this supposed to be a solution to world's poverty? As we've seen if support is provided or better said lack of counter-measures you may experience a continuous stream of migrants(i.e millions). Even if we want, we can't welcome everybody, I fear we can't coup even with the people who really need help, let alone the economic migrants.
On the other side there is also the cultural issue. Millions of people change the landscape for sure and the natives don't want to compete with migrants(why would they?). UK is leaving EU because of european "migrants" so it's not something to ignore.