Bungees are kind of getting a bad rap, here. I've used paracord, straps, elastic tarp cords, elastic cord with carbiners, elastic cord with velcro and bungees. I've had success and failures with probably all of them. Just last week, a strap adjuster on my commuting pannier broke, sending the bottom hook into the spokes.

Whatever is available and works for a given situation. None are perfect.