I guess it's important because momentum is a vector, and the debris fly off in a direction on average opposite to where we anted to push it, so this also means that the momentum of the asteroid itself has been changed by (at least) that negative ? But why is this better than a perfectly inelastic impact without any debris ? Was a significant fraction of the asteroid blown away ?
You can apriximate the debris to rocket exhaust. There isn't an engine bell to direct it and make it all leave in the most efficient direction but it's still thrust.
