I can't help but wonder how many people with plenty of "curiosity, passion, hard work, and persistence bordering on obsession" we've never heard of. In other words, we don't actually know--and likely can't know--how likely people with these traits are to be remembered by the world as geniuses, and how many will be regarded by their families and friends as obsessive workaholics with lousy personal lives and utterly forgotten outside those circles.
Reminds me of the string theory physicists that I read in some book.
Before string theory was established, there were two thoughts in physics, both equally challenging and one was string theory and the other quite similar. Both scientists worked in the two thoughts, had offices next to each other and created a lot of ideas and work from that.
However, string theory took off the guy who created it got lots of attention. His colleague who worked equally hard failed because he was unlucky to have the opposing theory.
We define genius by their impact on society and not by their inherent capability.
However, all geniuses are obsessively hard workers are a little vague. I remember Nash (game theory) only worked like that for a short period of time. By luck his work became very successful but he didn't have a lifetime of drive and passion because he was battling psychological illness.
Even the great genius Einstein had great four years and nothing else. Before those four years, he was a failure. After the four years, he never created anything and couldn't appreciate the modern advances in the field that he had created (god does not play dice).