If we can bust a rock up enough, even a large one, and increase it's surface area, the air will burn it up. It's just has to be fine enough.
That could work for smaller objects, especially "loose rubble piles" and the further away it is done the better, preferably far enough that most of it doesn't hit the Earth or atmosphere at all. One of the reasons early warning is so important.
It won't work for larger ones closer to Earth; the amount of material can be so large it heats the atmosphere, dangerously, even where few pieces are big enough to reach the surface. Not sure about risks to satellites, ISS etc with a disrupt and explosively disperse approach. Diverting them is the other approach, again best done early.
I expect it will be on a case by case basis. It does seem like NASA is looking for potential collisions in every asteroid's orbital characteristics, looking many orbits into the future; this is for the bigger ones. Lots of time to act. The smaller ones only seen as they approach don't give much time. Anything large from outside the solar system will be a serious problem, likely higher speeds and harder to determine their trajectory until already close - but those are exceptionally rare.
Bennu's track is probably known better than any other asteroid courtesy of Osiris-Rex and isn't a danger. 2024 YR4 needs some dedicated observation to track it's trajectory more accurately. Most on the danger list get crossed off with more accurate tracking.
The options seem to be deflection or disruption - and possibly combinations like blowing out material directionally to deflect. For energy delivery nuclear weapons give the most. For rockets used for pushing or pulling (gravity tractor) the rocket power needed and amounts of fuel get very, very large. Current rocketry would be struggling to deliver a few warheads and rockets and fuel for pushing/pulling beyond our capabilities.
If 2024 YR4 does turn out to be on a collision course I think we are not well prepared and even a crash program (hah) would struggle.
Planetary meteor defense that will be effective is a long term objective that is, by itself, extraordinarily ambitious, requiring ongoing improvements in rocketry and space based capabilities and international cooperation - but one actual impact of significance would be a big wake up call. I think colonizing anywhere is getting ahead of our selves but pushing ahead with planetary defense will always make sense.