Yes, that would be the conclusion I would also come to, it's just I'm not to sure how valid I personally find this one, because for example you Alex are yourself in a relationship that will never produce any children, are you that sad that this is the case?
On the other hand humanity has proven to be quite adaptable to catastophic situations, science for example would try it's up-most with artificial reproduction (so there would still be hope therein) and I think many people would just shift their priorities...
I think you just wrote the most uninteresting movie ever.
Humanity can't reproduce.
Humanity finds a way to reproduce.
I read this thread on Something Awful one time doing this exact thing. It was "The Shortest Movies in History"
The Lord of the Rings
Frodo: What's this ring, Gandalf?
Gandalf: Oh, that's nothing. Ignore it.
Frodo: Ok. Wanna play frisbee?
Uncle Lars: We need an Artoo unit; pick one out, Luke.
Luke: Okay. This orange striped one seems to work.
But getting back to your question. The central point seems specious, and I thought about the same thing coming out of the theater. But then I remembered it was a movie, a sci-fi movie at that, and sometimes you just have to swallow that central premise if you loved the movie otherwise.