Stirring is not needed while the yeast are actively fermenting because the fermenting wort is naturally turbulent - i.e. it self-stirs. This churning mixes the wort ensuring the yeast are suspended more-or-less throughout the wort, so they are always in contact with their food supply, making additional stirring redundant.
The turbulence in the wort comes mainly from the CO2 released, and to a minor degree from temperature differentials in the wort. The CO2 attaches to solids in the wort/yeast and causes it to rise to the top. When at the top the CO2 bubbles are released and the solids start to sink back down. As the solids sink, they provide a nucleation site for more CO2, or the yeast itself produces the CO2, and the process repeats.
Stirring/rousing is only needed when fermentation has stopped prematurely. If the yeast drop out early, then a little stir, or rouse, accompanied by a small increase in temperature can help get them started again. That's the only time you need to agitate the beer.
When it comes to speeding up the maturation process, that's really a function of the quantity of yeast, the temperature, and the enzymes available to the yeast. Stirring will not change any of these factors. To speed up maturation, commercial breweries can add enzymes to the primary fermentor, such as α-acetolactate decarboxylase which prevents the production of diacetyl by converting α-acetolactate directly into acetoin.