The long term goal that the oligarchs are looking at is to replace manual labor with robotics. Birth rates are declining throughout the world, including the Muslim world and sub-Saharan Africa. Countries like Nigeria are still well above replacement rate, but are declining. The birth rate is at 1.95 in 2026 and has been on a decline since 1970, when the rate was 6.75. As robotics replace functions like home cleaning, construction, and driving, the utility and cost benefits of immigrant labor decline.
What you say is true - or rather will likely be true in the distant future - but hype aside, robotic aren’t anywhere close to being able to replace unskilled or semi-skilled manual labor with machines anytime soon (except for completely repetitive, mostly stationary tasks like putting a bolt into a single assembly line unit). With such technology decades away, the oligarchs need cheap and obedient wage slaves. Westerners want high pay and rights, and so are too uppity to perform this function, so in the meantime, the more Third World people breed, proliferate, and invade, the happier the oligarchy will be.