In automatic transmissions some parts need to be moving with the engine in one moment and in the other they need to be stopped. Why don't transmisisons then use detent clutches to accomplish this?
Detent clutches use mechanical interference to force the halves of the clutch into hard engagement. The wear surfaces in this case are metal-on-metal which works well when the engagement duty cycle is low, as for example in the overrunning-clutch mechanism used in motorcycle starters.
However, for purposes of shifting gear ratios in a car transmission, you do not want hard engagement because it jolts the car whenever a shift is made. Furthermore, the duty cycle of engagement and disengagement is high in a car transmission, which means the engagement surfaces will wear themselves out of tolerance before the desired service lifetime of the transmission as a whole has been met.