I've always had an even worse idea, ethically speaking, that I think would combine well with yours : the first generation would raise the third, as you said, but that third generation would be born out of the frozen gametes of the now deceased zero generation.
That way, embryos would only be created after the death of both biological parents, which would give you whole lives to look at to decide if you wanted these persons to reproduce.
That would open the way to some interesting possibilities in directing human evolution while opening a whole new world of horrific abuse and creative eugenics.
My neighbor is in his 80s and we live in what used to be a rural area before urbanization caught up. He told me there wasn't any garbage collection, they put rubish in a small bin and just dumped everything in a hole in the garden when the bin was full. They didn't use any plastic so everything would just decompose. When the hole was full they'd dig another one and that was it.
In rural areas they commonly composted the organic garbage and burned much of the rest. Food scraps were also fed to animals so there was generally very little food waste.
My uncle used to pick up all the food scraps from a local restaurant and feed those to his pigs. It made a mess in his pickup truck, but it was a lot cheaper than commercial pig food.
We still do it. Every kitchen waste goes to the chickens, everything that's compostable goes to a pile in the back of the garden. With two adults we have about three bags going in the recycling bin and one bag in the garbage bin per month. We still have a bit of progress to do by buying less packaged items.
I have a PhD in physical chemistry and I've managed very varied projects ranging from designing machines to industrializing their production to developping new laser-based processes. Now head of R&D for a startup, if you want a quick chat you can send me a PM.
That way, embryos would only be created after the death of both biological parents, which would give you whole lives to look at to decide if you wanted these persons to reproduce.
That would open the way to some interesting possibilities in directing human evolution while opening a whole new world of horrific abuse and creative eugenics.