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.
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.
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.
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.