Entirely unnecessary. Native population growth rate is negative in every affluent country in the world, and they maintain their populations only via immigration.
Focus on improving the quality of life in third world nations (via investment, education, etc.) and growth rate will naturally fall, like it has everywhere else.
Though 100% social security and retirement security as a right has been theorized (at least in science fiction if not reality) to greatly discourage using kids as a retirement insurance policy.
I'm right up there with you on increasing global prosperity and raising the bottom though. That'll fix so many ills that achieving it would be a true benefit to everything.
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Additionally - cheaper energy (my first two unpopular points) should be one of the theoretical routes to getting to this kind of outcome. Having enough energy means that all sorts of other things become economically viable.
There are a number of currently less than popular steps that are obvious short / middle term answers.
Longer term I feel that as a species we need to take bigger steps. The problem with solar rings is that while they're great at focusing the sun for industrial uses like power plants or maybe solar forge operations, they're also great at delivering lots of energy to places that don't desire it. Like the evil villain in a cartoon, movie, or distopian dictatorship. I think they should be staffed the same way that other dangerous engineering operations should be staffed. Engineers and security forces working as part of the largest collective governing units (at the present time, that would probably be the UN or one of the permanent members on some UN security councils).