Your alternative is to shoot them at the border, or film them while they drown at sea... and even that wouldn't work as well as you might hope. Just wait and see what the next few decades hold, it's going to make this recent wave of migration seem absolutely delightful by comparison.
We've made the implicit choice to live our lives in such a way that the AGW is going to make the places like Northern Africa utterly unlivable, and then we'll blame people for fleeing from it.
It's the typical tragicomedy of a species that has a collective memory of about 20 seconds.