Getting it there would be one issue. Every kg of payload would require additional fuel etc.
Second, to drop things on to it would suggest being in orbit around it... which requires slowing the craft down from the c.6.6 km/s it was travelling. That would take quite a bit of fuel, which would need to be launched from earth and carried most of the way - up to the point the craft wants to slow down. Again, that increases the weight launch quite considerably.
That's just the issue with getting it to the point of dropping the payloads. It's an engineering challenge rather than an impossibility, of course, but that brings home the next question:
WHY, for the love of God, WHY??????
NASA are also confident that the asteroid and moon posed no real threat to Earth before the impact by DART, and will pose no threat after... but time will tell!
Chances are that it will likely have just altered the oribit of the moon around the asteroid very slightly. I think they're suggesting it will have shortened Dimorphos' orbit by 1%.
Bear in mind that even the smaller of the asteroids, Dimorphos, that DART impacted on, is some 10 million times more massive than DART. Yes, DART was travelling faster than a bat out of hell (assuming such creatures can't reach speeds of 6.6km/s), but the mass differential is like a 1/100th of a gram compared to someone weighing 100kg.
But, maybe... just maybe... if Dimorphos does split open, we may finally uncover where Trump has hidden all the other Classified material he supposedly took!
