If the population halves each generation the biggest problem is total societal collapse. The children and the elder cannot be sustained by a small number of people of working age and the infrastructure cannot be maintained by a dramatically dropping population: even with AI and robots, roads don't fix themselves and train tracks don't get fixed by robots. We will not even have enough doctors and nurses to care for the seniors and no economy to make retirement possible (money will be worth their value in paper as there will be no people to provide services and goods for it).
If someone things the population on the planet is too big, then plan for a reduction that is manageable and change the pay-as-you-go pension system that exists in most of the world, that is based on working age people paying the pension for retirees. Even at replacement rate the pension systems will collapse, they were built in a time when the average number of children per woman was around 7 and the age of retirement was higher than average life expectation.
> The children and the elder cannot be sustained by a small number of people of working age
No, the children are fine in this scenario, there are even proportionally fewer than now and so there are any number of available carers.
The elderly are screwed. But, that seems OK?
> If someone things the population on the planet is too big,
This isn't a centrally planned thing, it's just an exaggeration of the observable reality. On the whole humans who could carry a baby to term but understand exactly what's involved are not keen and if they're willing to do it once or twice draw the line there. The assumption that we're just not compensating them financially enough to reproduce more is let's say, not well supported by available evidence.
I think we should choose to be entirely OK with that until there's risk of a real population bottleneck, e.g. 1000x fewer people -- in the expectation that conditions change and it might sort itself out without action.
> The elderly are screwed. But, that seems OK?
Remember, these elderly will be most of us. IIRC many 20 and 30-somethings today will be still alive by the time shit hits this specific fan. How old are you?
Oh I'm much older than that. I'm definitely screwed, but I don't see why that means this is a bad idea ?