I just read an article arguing that we need very fast rockets for the deflection of comets, since we will probably detect them just several months before impact. So we need to hurry in order to pick them up as far away as possible. It explicitly motivates fusion rockets, since comets might be detected only 6 to 18months prior to impact.
That got me thinking. For the sake of argument, assume we have several ICBMs in orbit (political likelihood left out of this question). Assume they are armed with 500kt warheads. Furthermore, assume they are able to meet the comet 1 month away from earth and we want it to be deflected by 5 times the diameter of earth (60 000 km). So by my rough calculation we want to achieve a 23m/s acceleration.
The scary nuclear weapons calculator gives a vaporization of 140mm of (carbon) surface material for a detonation as close as 250m. That value more than doubles (330mm) in case of water ice. That seems to be quite a lot. That means the payload of a single Trident II missile could vaporize between 1.7m and 4.5m of surface material from a given comet. So for a water ice surface of roughly 4km x 4km that gives us a "propellant" of 72 000 000t of fuel. For your typical $10^{13}$ kg comet that should be 0.5/1000 of your mass (give or take). Assuming that our vaporization is at least as effective as a rocket engine (ISP 500 seconds) and crunching the numbers using a delta-v calculator that gives 2.5m/s delta-v.
So according to my rough calculations, there is no extreme advantage of a faster rocket here. How would a fusion rocket change the above principles? Why can't we simply put some 20+ Trident II like missiles somewhere in orbit (as I said, politics aside) and wait for a target to pop up? Where is my error? And if my calculations are totally wrong (which might well be), what makes it better to have a very fast rocket and get things done 6 months away from earth (couldn't we as well send 6 times the number of nuclear warheads with conventional slow rockets)?