I'm with you here. The RIM-161 standard anti-ballistic missile used by the US is quoted by wikipedia as having a speed of 9600km/h or 2.7km/s. Speeds in low-Earth orbit are about 7-8 km/s, objects entering from a solar orbit likely several times that. There is absolutely no way you would have significant success probability of intercepting it with a missile unless you knew the incoming orbit very precisely.
Just look at that dashcam footage: from entering the atmosphere to breakup was just a couple of seconds. On a very tangential orbit, no less.
By the time its left the silo. Russians are dead keen on their one-shot silos packed to the gills with various devices (pneumatic, hydraulic, explosive) to bring a missile up to ludicrous speed very, very quickly.
Spent a very enlightening afternoon down an old bunker near pervomaisk.
Found some stats in the tourist brochure from there. 9.4m high,1.1m dia, 4km/s in 4s, which gives an acceleration if about 102g. 80-100km range. Max speed 7km/s. "directional blast" also, which is interesting.
The US Nike-X Sprint had similar performance (Wikipedia says only 90 gravities, and there's some nonphysical-looking footage of test launches on youtube somewhere). Pretty crazy, and I gather that MIRVs made that whole category of ABM obsolete.
Just look at that dashcam footage: from entering the atmosphere to breakup was just a couple of seconds. On a very tangential orbit, no less.