Isn't that mostly survival bias at work? No matter what the odds were, the winners write history. If we had died out in one of the steps along the way, we wouldn't be here writing about it.

Once humanity spread around the world, the odds of a natural catastrophe killing all of us at the same time became very low (limited to planetary-scale distasters).

Only since the industrial revolution we've been on a more dangerous path toward central points of failure. On a geological time scale, that's only a very short time. But we've been testing our luck really hard.