If the world population dropped to half a billion, there wouldn't be enough wage slaves to prop up an economy in which trillionaire oligarchs are possible. If they really wanted smaller population sizes, they wouldn't be advocating free HIV and malaria drugs (at US taxpayer expense) to the Third World, or bringing in millions of Third World people into first world economies and welfare states in which many more of their children would survive than would in their native lands.
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.