little_lifter, an OL may develop a pattern where they are so fixated on getting under the bar to catch it (the third pull) that they do not get everything they can from the 2nd pull (from the pockets).
Often you will hear OL coaches calling out something like 'finish the pull'. They're talking about that 2nd pull and how the lifter might not be getting everything out of that phase, it leads to a situation where it doesn't matter that they are quick to get under the bar.... they dont have enough time because the bar has already started to amortize (stopped rising) and started to descend at a rate and to a position at which they cannot catch it.
I can see how addressing this is most easily done in the power clean movement. Let's say a lifter was cutting their 2nd pull as they worked up to their daily max or whatever is programmed for that day. Coach detects something inefficient. Instructs lifter to go back down and start power cleaning with a 2nd pull emphasis then the lifter starts working the weight back up again.
Regarding the elbows bending, the first 2 pulls are about extension at hip, knee and ankle; the elbow does not flex in order to create vertical motion on the bar. The elbow will bend, as Powerbuilder pointed out, as the third pull begins; when the lifter pulls themselves under the bar.
The other issue about the difference between the full lift and the power version is the nature of how the lifter squats. Someone new to lifting or whom has never developed much depth to their squatting will not be able to get the full return and ascent after receiving the bar in the deep squat position. There is a springiness and bounciness that many lifters have not developed and therefore cannot access then return onto the bar. This component of the lift, the stretch reflex, is how and why the 48kg women's olympic champion Chen Xiexia has put up 120kg in the clean and jerk.