I'm no expert and I have not analyzed the videos in any depth, but from what I hear the ability to function calmly under intense stress is a fairly significant requirement for that sort of job. Anyone getting panicky, or OBE (overcome by events), will be a problem and usually wouldn't make it through the selection/training process, I am guessing.
I don't think the height thing matters.
Re-holstering the pistol should be a natural smooth action acquired over 1000s of reps and should be second nature even under pressure, but maybe the holster position got jostled in the commotion altering it's position somewhat causing the fumble... who knows. Lots of things to dissect on this from any angle.
One observation; I thought they stayed at the podium for quite a long time in the dog pile. Getting off the "x" as fast as possible is paramount in any ambush scenario like this... Not knowing where the effective fire was coming from, I'd envision immediately dragging 45 off stage, by his ankles if need be, and moving as fast as possible to his armored truck. However, I can only imagine certain celebrities have difficult personalities (I need my shoes!) and are probably resistant to the best intentions of the detail to some degree. But I don't know their TTPs or what, if any, other protective means are in place that dictate their actions ... so take this for what its worth.