i think you basically want some amount of agitation at some point relatively early in the process just to make sure all the grounds are getting wet. then you usually want less in the middle/late phases to avoid clogging as op mentioned, since the undisturbed bed slows/stops a percentage the fines from reaching the filter, and the reason you want to avoid clogging is that you cant get as good of a result if it winds up running too slow overall.
pouring technique can definitely have an effect on all this (e.g. pouring too hard in the middle to late phases with a shallow water level digs into the coffee bed and churns it up causing a lot of agitation).