We're getting into pseudoscience here, but there are times to stir and times to not stir.
Blooming coffee is pouring 1-2x the weight of coffee worth of water over the dry grounds. Supposedly, it allows the beans to offgas the CO2 that builds up during roasting. Blooming is also called "pre-infusion" in some circles. Either way, it just gets the coffee ready for brewing and breaks up clumps.
For my Aeropress method, stirring accomplishes both the offgassing and something much more important- dissolving solids. Most brewed coffee needs a 15:1 ratio of water to coffee, but my method is about half that coffee at 30:1. The reason it isn't weak is because stirring helps coffee solids dissolve into the solvent (water here). With my method, there's a bell curve to the TDS and coffee strength based on the amount of coffee added. It gets weaker on both ends of 11 or so grams of ground coffee. On less than 11g because there's not enough coffee to infuse 330ml of coffee, and much over 12g it gets weaker because there's not enough water to dissolve the available solids.
I tend to agitate the Chemex as much as I can without disturbing the finer particles closest to the filter. They actually help the filter work and result in a cleaner cup. The other benefit is that it slows the brew process so the water can extract more of the caffeine. You want about a minute for the bloom and then 1 minute per 100ml of water added after. You dial in the grinder by timing how long it takes for the Chemex to drain. The Aeropress is a different animal and uses pressure to get coffee through the filter. It also works in less than half the time and uses much stronger agitation (stirring) to get the TDS up.