The idea is popularly known as "Rods from God," and Jerry Pournelle was an early proponent of the idea. I got the chance to discuss it briefly with him one of the times we ran into each other at Comdex, when that was still going on in Las Vegas. He's one of my favorite science fiction authors, along with Larry Niven, but Pournelle is also one of the very early PC columnists, going back to the very beginning in the mid to late 70s with kit PCs. I used to see him at least once a year from '77 on when I got involved in the first sales of pre-built PCs out in San Francisco. He was always very nice and generous with his time.
In addition to being an SF author and journalist he was also a member of Reagan's advisory panel that came up with the pieces of SDI. These kinetic energy weapons were considered as a viable weapon at that time as well, seperate from the SDI developments as this implementation doesn't deal with missile defense. There are kinetic energy parts of missile defense and their development is pretty much all that's left of SDI, except for the airborne laser, which should be available relatively shortly, and THEL, which we co-developed with the Israeli's. Rumsfeld was around back in the Reagan administration too and he's revived this version of the "Rods from God" specifically with the idea that they can be utilized against heavily dug in facilities, such as in Iran and North Korea. This 2005 article from The Weekly Standard covers that and other points about the system nicely.
Despite no radiation, large impacts have much the same deleterious effect on climate.
There are lots of sizes of rocks to drop. You choose the size depending on the effect you want. For me the point is that once we can move the asteroids around and mine materials from them we don't need to loft anything from Earth, even if we want to implement the "Rods from God" idea. We can get the material from mining the asteroids, or simply grab a rock of the right size and of a good enough shape and material to give us the effect we want. Pournelle and Niven used the idea extensively in their novel Footfall, from 1985. I think that is the ultimate "someone invades the Earth" book. They covered the topic of a natural comet impact in Lucifer's Hammer, from 1977. It has a fabulous description of the comet impact using the analogy of a huge hot fudge sundae. If anyone wants I can post that. I've already posted probably a lot more than people want to slog through and it's about 1,500 words, or 4 pages in Word. But it's a hoot.