I was thinking about the rotation problem the other night while watching a show about this sort of thing and noticed they never talk about the fact that they’re tumbling through space.
To me that leads me to think that maybe some sort of mass driver or low thrust propulsion might be better because they would only push when the asteroid is oriented correctly.
OTOH a large enough gravitational tractor parked at the right distance could probably overcome the complex moving gravitational field of the asteroid.
It wouldn’t be as efficient, but it *might* be more practical. The problem with it is, the propulsion would have to be not strong enough to break away from the grav, while being strong enough to maintain a steady distance and steady tug on the rock. IOW, it would require a very long time frame to work, and experience teaches that we simply won’t have that long a time frame in which to work.