File this under "Things still too radical to say in 2018."
Honestly, your proposed solution goes too counter to human nature to be viable, in my opinion. Not to say it wouldn't work if you could pull it off, just that there's too much going against it.
Human nature is selfish on a per-tribe basis. I think much of humanity's ills stem from our inability to effectively care about more than ~100-1k people. Even if you convinced the world to go along with this, including the inevitable rash of unrest by religious groups and murders/etc by people who feel they were unfairly sterilized, here are a couple questions I have with this plan:
1) Age distribution +30 years out from implementation? Developing nations with declining growth rates (most of them) are facing serious age-related care and resource issues as the largest section of population becomes elderly. The plethora of energy and real estate wouldn't kick in until the sterile group shuffles off, and the preceding ~10-20 years would be a really uncomfortable transition without some serious forced old-people-warehousing solutions. Even from just a "how many care nurses can we really get in here" point of view.
2) How to implement permanent, lasting cultural shift on wealth, growth, and sustainability? The mentality that led us here, that maximum growth and wealth is more important than sustainable growth, would have to be permanently squashed from the human psyche, otherwise it's only a matter of time before the "chosen ones" and their progeny get us right back where we started. I don't think anything is permanently squashable from the human psyche, especially things that lead necessarily to occasional "my tribe has to take a haircut so someone I've never met can improve," due to afore-mentioned tribal nature of humans.
There are more, but I don't have time to think of them. I would like to revisit this later, perhaps.
Personally, I think we need to re-organize society to be more in line with how humans are wired, then build-in rules and solutions for sustainable growth. Like designing society around many more, smaller towns, linked together by internet and services that make sense as national services (like risk pools, transportation networks, etc.) but are as close to self-sufficient as possible in terms of energy, food, and water. I don't know what that society would look like, or how to get there, though.