Capital flows completely freely between borders, but people can't. I don't really blame anyone for being economic migrants - they're just refugees of a different type.
However, particularly for European governments, it's now becoming visible that there is a selection to be made: you can have completely open borders, or you can have a welfare state, but you can't have both.
Depressing future scenarios like this make me miss the 1980ies, when popularly feared terrible futures had clearly good solutions ("don't blow up the planet") instead of a choice between two evils.
It does not have to be like that, it is just what you believe.
Does bettering oneself mean the same thing for economic migrants as it does for Europeans, in your mind? I gather from your comment that it means "attaining greater material wealth" for economic migrants. What does it mean for Europeans? Does it mean sharing their material wealth with the less fortunate, at their expense and the expense of their progeny?