Tim, I think each person is—indeed—destined for greatness. The fault lies in our societies definition of greatness which includes fame and notoriety as a precursor for greatness. Sometimes the mundane is the greatest source of a life well lived.
To me, the father who plays with his kids after he gets off work, provides for his family, and who’s kids love him is an example of greatness. God knows it’s mundane, but any dad will tell you the absolute mental hurdles and exhaustion you have to face when you’re present 16 hours with work, kids, wife, chores, etc etc. To have kids who grow up and say “Dad loved me” despite his utterly mundane existence? Man, that—to me—is greatness. And noted it was formed in the fires of hardship.
Each of us have a role to play in this life and sure, some will achieve their 15 minutes of fame. But like the Jesus’s parable of the talents, the question of greatness is more what we do with what we’ve been given, and sometimes that just being a good parent, epic neighbor, or great worker.