For CDAF, the computer absolutely needs to tentatively alter focus to even arrive at any decision on how to proceed in focusing it - especially to ascertain in which direction to focus. Only closed-loop operation (doing and testing) gets any results here. It's like an operator trying to focus on a ground glass screen alone.
a PDAF system is more like an electronic rangefinder that supplies the computer with an estimate about how out-of-focus the image is, and whether it is focused too close or too far, before needing to do anything mechanical. This way, the coarse focusing can be done open-loop and in one step, only requiring closed-loop action to refine. It's like an experienced operator using a split prism rangefinder.
These two methods pose very different requirements regarding responsiveness, precision, speed, speed penalty of changing direction, hysteresis when changing direction, settling times/dampening... to a focusing drive train.