No. But you don't know how far behind they are when you dispose of it. It only becomes random plastic after they've lost your trail.

> can just deface it in any way and throw it out the window on a highway or into any trash can

Sure. Or you can keep it until it can be safely disposed of. Which carries fewer risks? We don't even have to hypothesise, we know for a fact that the IDs on his person didn't cause him to get caught. We also know him not having the IDs on him wouldn't have caused him to be less caught.