There are two factors. First, any missile with inertial guidance needs to have a precise angle reference as a basis for the guidance system. If the guidance system starts off slightly wrong about which way is North, it's going to miss the target. Second, the guidance system in Minuteman I could only turn about 10 degrees from its initial angle before the wires would get tangled up. The solution in Minuteman I was to use the launch azimuth as the reference angle, so it was precisely lined up against this angle. Most of the alignment was physically rotating the missile, but the last bit of alignment was by constantly rotating the stable platform for alignment with the light beam from the autocollimator.