Old people aren't useless just because they can't reproduce, or because their physical bodies are undergoing decay. By that logic, you'd have to execute the gays, people who abstain from sex, people who have decided to never have children, people who have had vasectomies and had their tubes tied, and people with serious diseases.

If we're going to kill off everybody who is "useless", then somebody has to decide what qualifies as a "useful" person. In practice, this always ends up being some bureaucracy with little insight into the real value of human life and human experience, who will just start another Holocaust. And what you'll be left with is not a master race of Ã?bermenschen, but a twisted society of heartless individuals, or (more likely) a swift and powerful revolt against your tyranny by the masses.