The refugee theme did not seem to gibe with the infertility theme.
I think Cuaron was mainly interested in doing a refugee themed film and the infertility angle was something he just had to deal with as it was the plot of the original novel.
I don't think refugees would have been such a huge problem in a world that had seen 18 years with no children and a constant death rate. Supposedly 155,000 people a day die globally. That means that the world had lost 1018350000 people since the beginning of the infertility crisis. In THIS world, likely more due to the global violence. SO with over a billion less people in the world, would refugees really have been a problem on that scale?