I wonder if others have different interpretations. The problem that agitation is supposed to solve is uneven distribution of active ingredients, and it must do so in our case before the distribution becomes uneven enough to cause uneven development. If unevenness is desired for some esthetic purpose, it usually is not random unevenness but somehow proportional to density of the developed image. That is something we cannot control in the way a painter controls the image, so we hope the developing solution does it. Periodic agitation, it seems to me, should be vigorous enough to restore the distribution of active ingredients to initial conditions before the random changes induced during agitation can produce unwanted random changes in the image.
The products of development cause local changes in the development rate that may wander from place to place due to local changes of specific gravity. Every chemical reaction is likely to cause local changes in temperature as well as chemical composition that result in changes of specific gravity. These changes have rates that are generally reduced as the concentration of active ingredients is reduced, so we have learned that we can extend the time between agitation periods by using less concentrated developers.