The majority of immigration to any given Western country comes from areas that have either been colonized by that country or else stand in a looser relationship of subordination and dependency. While presumably there are still at least two or three people who believe the ideological bullshit of the “civilizing mission,” most adult human beings recognize that the whole point of colonization and subordination of other countries is to gain access to their wealth and resources so that they can be expropriated for the enrichment of the colonizer or dominant country.
Hence it’s not just that the target country happens to be rich while the immigrant’s home country happens to be poor (or, I might add, in political turmoil, in a state of civil war, etc., etc.). Those conditions hold in the home country because of the destructive effects of Western involvement — not just during the era of “official” colonization, but on an ongoing basis. People generally don’t leave prosperous, self-sufficient countries en masse in order to drive cabs and clean hotel rooms in a foreign country where they will be hated and scapegoated.
Rather than recognize this simple truth and act with some basic human decency, though, the former and current imperial powers choose to demonize the immigration their own exploitative and unjust domination has produced — and they would rather let the people whose nations they continue to despoil drown or die in the desert than let them drive those cabs and clean those hotel rooms.