>>126565131X The Last Woman would be focused on some individual person with a background, personal relationships (boyfriend, crush, whatever) and family - shoehorning in some connection to science, politics (a dad who's a senator?) and other shit. In Y, really unrealistic bullshit like secret agents being sent to protect him, roving gangs with sudden complex ideologies, invading nations for some reason (as if they wouldn't have their own fucking problems) in order to make an extremely broad high concept story interesting. High concept doesn't have to be difficult or complex, it only means a story deliberately limited to a simple premise or theme (think Jaws for a good example). Fact is, Y sucks as high-concept and the writer focuses on unrelated interpersonal drama which is sort-of realistic in the sense that humans are generally too self centered to comprehend global events or issues.
You could do X the Last Woman essentially the same with the same story beats if you want to mimic the lazy, pretentious, hackwork of the original. But if you were trying to write a GOOD high concept story where all men or all women died mysteriously you would first have to account for the basics. Four billion bodies would be rotting and lots of work would be needed to clean it all up. Up to around twenty percent of men would probably suicide immediately, leaving around 3 billion humans left. Chaos and disorder, gang leaders would immediately try to seize power, local governments would immediately draft people into emergency civil defense to fight them, everything would be mobilized and food shortages would slowly accumulate, manufacturing might completely stop, internet would shut down, religious nuts would begin forced conversions on their neighbors, scientists of all kinds would be blamed and executed by roving mobs. Majority ethnic groups would try to push out or execute all minority groups. However, 99% of all heterosexual male motivation would evaporate.