"Infinite leisure", what is meant by that? I believe that the author foresees a world where robotics and computer automation replaces every need for human labor. If so, we would inherit the blessing of infinite leisure. Maybe. But consider for what purpose beyond our basic needs would that automation be used? This would depend on human imagination which cannot not be replicated by any algorithm. John Quincy Adams once wrote "I am a warrior so that my son can be a merchant, so that his son may be a poet". Once we are secure, and all our our material needs have been fulfilled and more, we will still need to inspire and entertain ourselves, lest we die of boredom.
The focus on flying was the hook. There is no such thing as infinite leisure. Unless there are extraordinary circumstances, nonfunctional humans won’t mesh with the future unless there are mitigating influences (power, corruption, etc.). Humans won’t become obsolete.