The more accurate you can make the nuke, the smaller it can be. Saves you nuclear materials and launch weight.
And against hardened targets like missile silos or command bunkers, pretty accurate (eg, Cheyenne Mountain couldn't withstand a direct hit, but it could a nearby miss. Colorado Springs would be toast either way.)
ICBMs are pretty much autonomous once launched (I would assume/hope they have an abort mode), but their targeting data is updated regularly (especially true for sub-launched missiles, of course, but also for the independently targeted warheads on a MIRV.)