Do coffee and tea need to be agitated while brewing?
Tea and Coffee contain a spectrum of flavour compounds and most certainly, not all are pleasant.  

If you've ever had an over steeped tea or over brewed coffee you'll know that the optimum extraction point is long before maximum extraction. Where you are no longer extracting just pleasant compounds and picking up higher concentrations of things like caffeine, bitters, etc.

Agitating tea or coffee runs the risk of (or facilitate) reducing the time it takes to extract the unpleasant part.  On that front, experiment with not yo-yo dunking tea bags and squeezing the tea-bag with the back of the spoon (mild forms of agitation) to see the taste difference.