I am the OP for this topic. I thank everybody for your interesting perspectives and ideas. But djb has nailed a telling point: even people who are careful can make mistakes, with potentially disastrous consequences.

For twenty years plus, I strapped a bungee cord or two to the rear rack. During all of that time, thousands of rides, and tens of thousands of kilometres, I never had a problem. But the one time I was a little sloppy, I came close to an accident:

I biked to the grocery store after dark, strapped a large package to the rack with a bungee cord, arrived home, and put my bike away. But because it was dark and I was tired, I released the cord, took the package, and went inside. The next day, I hopped on my bike and rode off, with one end of the bungee cord dangling down. I rode for 10 or 15 minutes when the cord hooked itself to the rear hub.

Maybe the lesson is that it's worthwhile to do a quick visual inspection before stepping on a bike. Interestingly, I already do this... but the rear rack and bungee cords were not on my radar. I almost always feel my tires to ensure they are inflated enough, and before I pedal too far, I always test my brakes. The corollary, for anyone who chooses to strap bungee cords to the rear rack, is to always ensure the cords are secure before starting to ride.