Counterpoint - [in Western countries] those who have any chance to promote population restriction are "the 1%" and don't care provided the population can be controlled enough to keep working for them.
We've had a massive energy boom in the C20th, and grown fat from it, and now realise that's not sustainable for the planet. We can't continue that growth.
Robotisation will continue the current trend of increasing the wealth gap. And we don't have the energy or resources to just buy our way out of it by making more and more junk to sell (as per C20th).
Yes more immigration, or more pay for immigrants, increases demand from them for "middle class" luxuries (and reduces the ability of the native population in general to pay; but doesn't reduce the desire, and debt fills that gap), but we need to take the limitations of the planet in to account and realise resources aren't as infinite as they seemed - that means it has to be treated as zero sum, and indeed with restrictions on energy/resources that debt won't be there to cover things.
On top of this the ability for the Western nations to control others, and live better off their labour, seems to be finally ending.
IMO if we in the West want to maintain our current standards of living we'll need to entirely curtail population growth. Redistribution is going to hit hard, except for the robot owners who will get richer.
Regular Westerners (the 99%), to my view, will have a taste of living in a World where others have the wealth, and we don't have resources (skilled labour in particular) to bargain with - the elite won't need most of us. Heavy immigration can be a foretaste of that. Skilled immigrants allow the elite to bypass negotiation with their own populations (that might lead to democratisation of roboticisation benefits) whilst simultaneously leaving home countries devoid of skills and ripe for exploitation, not by nations but by the Capitalists.
/rant