For the "larger ones" that fitzwatermellow was mentioning, the problem is that your mental model of a big rock starts breaking down. You'd be closer to think "big gravel pile sort of iced together, sort of held together by local gravity because there's nothing else pulling them apart". You shoot a little pulse at the gravel pile and break a piece off and it may simply fly out into space, taking almost all the momentum with it and not affecting the bigger body at all. You apply a big force and you might just send rocks through the pile, with, again, the rocks going through taking most of the momentum you applied with them. (Same for landing a booster on it... there may be nowhere you can boost where the booster doesn't just drill right through and come out the other side.) Hit it harder and it may simply spread out.

The advantage of the gravity towing approach is that gravity affects the entire pile equally; it doesn't matter how tenuously the whole thing is held together. This approach could literally deflect a mountain-sized ball of pure sandbox-grade sand, completely and correctly. That's not something a lot of other approaches can say. It's only downside is that it's miserably slow, so you have to call the problem years in advance.