Just spent some time crunching the numbers and the number of migrants (6 million) is the equivelant of the number of working age people in the UK that were classed as capable of work in 2017 (OK I didn't get the actual number but I took a third of all adults who were out of work which will do). I think Sweden is said to have a 16% migrant population so what's stopping the rest of the west from taking on more?
Politics. Media.
Eventually they will be forced to somehow attract migrants. Some projections shows that Balkan countries in the year 2100 will have half population as of right now. So unless they will offer good condition to migrants they will ignore them and move in other countries that will offer them better conditions. Second part of this century will be a huge fight for migrants. Countries that will not be successful at attraction them will become half empty and lose they strength a lot.