> I often wonder if John Galt ever found himself living alone in a room with no one to take care of him in his old age.

I hope you understand that to Objectivists that sounds like saying "I often wonder if Frederick Douglass ever found himself suffer an accident at work with no master to take care of him because he isn't a slave".

I am sure there are better arguments possible against objectivist position, but the one you made is rather naive one.