First, they would replace us. I’m reminded of a Larry Niven story were a billion-year old alien ( she spent most of her time near lightspeed, with slowed time ) mentioned visiting Earth early in her life, and speaking with the locals. It turned out that Earth was previously dominated by a slow-living intelligent anaerobic ( non-oxygen using ) species. They were destroyed by green goo, as it were; green algae evolved, filled the air with oxygen and killed them all.
The second difference is that nanomachines, depending on design, might be unable to evolve; thus the “grey” term. They might eat the biosphere, and just sit around until the sun dies, never doing anything interesting.
I’m betting this has been done, but what about a scenario where no further children are born, a scenario that becaomes referred to as “The problem”. The drop-off in childbirth would be precipitous, and as the population ages a sense of dread and desperation grows as more and more resources and attention are turned to the “The problem” (e.g. schools and universities begin discarding all education unrelated to “The problem”).
I’d particularly be interested if it was clear than no life was ended prematurely by “The problem” itself; the only thing that was being lost was one’s legacy. I’d find it interesting to see if/how the value of something one can never own could rise to a point where it is all-consuming.
I think, though, this might work better as a book (too philosophical for the multiplex, plus there’d be far too many characters outside the 18-34 demo).
I don’t think that it’s so much that they’d be unable to evolve, it’s the fear that any evolution is unlikely to return to complex and intelligent life forms.
The book Implosion, from 1972, by a Dennis F.Jones, is one about a scenario with decreasing fertility, and what happens to society. I think the cause was finally discovered to be a bio weapon of some sort, that got out of control. Fertile women end up being placed in camps, are kept constantly pregnant, and so on. Their husbands can divorce them. I think, by the end, that it’s discovered that the first generation of girls born after the problem started is bearing only boys
It could easily be made into a movie I suppose, it wouldn’t even need any fancy special effects.