Dear Flavio,
My most unwelcome primary conclusion is that our basic ethical perspective and perhaps also the perspective taken in mathematics and physics not just by the Perimeter Institute deserve scrutiny without taboos and most likely corrections.
I confess having killed my possible sibling when my mother asked me whether I would like to have a small brother or sister and I replied this was perhaps no good idea because of the situation in which we struggled for naked survival. Certainly she felt as did I.
As a secondary conclusion, you and I agree that birth control is the only acceptable way, and voluntarily control is better than China's one-child politics. While you wrote: "the emancipation of women in countries where they were having many children...", I see the development of contraception a decisive step and disagree with you: Isn't the birth rate still much too high in many poor countries, in particular in those where an aggressive religion demands as many believing children as possible, e.g. Boku Haram in the north of Nigeria. Rich regions in Europe and Northern America have already small birth rates.
However, I maintain my unwelcome question:"What do you mean? How many people does the Earth need?"
Isn't it irresponsible to blindly trust just in the regulation by money, spoil all available raw materials, risk national conflicts between military strong nations like the veto power China and weaker ones like Vietnam, calculate e.g. the costs of nuclear power without consideration of carefully handling the wast over thousands of years to come, polluting air and water in irreparable manner, etc.?
While killer robots are certainly effective means from a national perspective, the perspective of the whole mankind restricts their justification.
I don't hide my logically based preference for the latter point of view.
Let me stress again that I am dealing with immature basic views behind all that.
Discoveries and inventions must not be misused as to merely mitigate consequences of going on with national heroism, wars, denial of causality and all that.
Best,
Eckard