Agitation serves two principal functions.
1 ) the most important is to ensure fresh deveper contacts the surface throughout the process.
2) to ensure that any debris and bubbles do not block the contact of film with developer.
How it should be done is a many part answer.
Up to the 80's and before many studios owned their own processing machinery
The most used developing method used by professionals for roll film and sheet film was by using 3gallon tanks with stainless cages and film holders or ss reels.
in all cases the agitation was by completely lifting the cage clear of the developer and returning it to the developer.
then importantly banging the cage sharply against the tank a couple of times to shift bubbles.
how often this should all be done is not that important. But it should be regular and always done exactly the same.
stand development was used as a method to increase shadow detail whilst holding back highlights , but more often used to increase edge sharpness when using thin slow films with dilute one shot developers. (It creats edges very like digital unsharp masking, and taken to extremes with complete halo lines.)
Stand development works because the dilute developer soon become exhausted by the dense highlights, so ceases to work on them. The shadows in the mean time have plenty of chemical agent left and will continue to develop. At the edges there is a migration of developer ftom the shadows to the highlights, giving the typical edge effect.
Some agitation is needed but will largely depend on the equipment and skill of the photographer to get an even result.
After 1952, when I discovered stainless reels, I never used plastic ones again Plastic reels are the invention of the devil and are the main cause of uneven development, streeks, scratches, stress marks, contamination, fingerprints and buckled film. In a race with a fellow professional I once loaded twelve 120 film reels in the time he was still on his third patterson one.
Like many chemical processes development is time and temperature critical. From a photographic point of view this time produces the required gamma or contrast. This is more important than the secondary density. ( density will be correct if the exposure given was correct) it is bad practice to lenghten development to increase density, as this will also add contrast block highlights and increase graineness.
for those that do not know metal reels are wound on from the inside out.
they never become stuck as they never need be pushed along plastic grooves.
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