Asteroids torn apart by Earth
The rotation curve for an asteroid is often determined by measuring the change in brightness of an asteroid over time. Plotting the light detected versus time yields a somewhat sinusoidal curve, which is usually interpreted to be due to the rotation period of a non-spherical asteroid. If binary NEAs are common, then what some of these light curves may actually be showing is the orbital period of the binary system (if they are synchronous this will be the same thing as the rotation period of the smaller component). This could mean a new interpretation of what may be behind some of these light curves.
As a further comment, the existence of double impact craters is not necessarily suggestive of binary asteroid systems -- an asteroid is more likely to break apart when it actually enters the Earth's atmosphere than in more distant encounters, so it's probably not good to assume that the system had already broken up and become a binary during a previous encounter.