Your sentiments were shared by a Roman Emperor in 376 AD. That's when Emperor Valens allowed some Goths, claiming to be seeking refuge from the Huns, to cross the Danube into Roman territory in Thrace. Valens believed the Goths would benefit Rome by providing troops and taxes.
But more and more Goths, who Valens did not permit to enter, quickly followed anyway and a controlled resettlement snowballed into a massive flood. By 377 the Goths attacked and defeated Roman army units in Thrace.
By 378 the Goths joined forces with the Ostrogoths and the very same Huns that Rome gave the Goth refuge from. They then attacked the entire eastern Roman Army and killed Valens along with 2/3s of that Roman army.
By 410 the Goths attacked and sacked Rome. Within a few decades, the entire Western Roman Empire was overrun and occupied by various barbarian tribes.
What turned out to be critically and historically important was not why Rome allowed the barbarians in... but the real intent of the Goths in coming - which was quickly revealed in their ever escalating hostile actions.
Sound familiar?
"Not really an invasion, just the price of empire." Ha!!!!! It is not possible for a person to be more wrong.
The North Africans didn't go to Belgium seeking refuge. The Belgians actively recruited them as laborers and invited them into the country. You analogy to the Romans and Goths is flawed.
I'm not trying to downplay the problems caused by the recent flood of immigration to Europe, but the terror attacks in France and these in Brussels were carried out by born-and-bred Frenchmen and Belgians.