Immigrants do not compete with native workers because they have complementary skills (like different native languages). The evidence is very very strong that immigration does not decrease wages. It generally increases them because it provides new demand, though that's not guaranteed.
Our immigrant ancestors were almost all unskilled. I’d rather the government not tell me where I can or cannot live, as a matter of basic human freedom.
Works great for the upper classes - keeps the price down for those fancy Michelin dinners.