I've been using the same webbing straps for 20 years, first backpacking and now bicycle touring. I don't mean the same type or brand I mean literally the same two plastic buckle straps. I don't know what they're made out of but they don't look any worse for 20 years' wear. I've never had a load secured with those straps come loose or move around. I can't fathom packing in a way that would permit a strap to get caught in a wheel.

All that said, and my previous "universal' comment notwithstanding, I do use a bungee to secure yesterday's wet jersey and my flip-flops just because it's quick and easy and those things are light enough not to bounce around.