The jerk dip is a natural reaction to absorbing the force of the landing while trying to maintain a "punching" gymnastics term wise to connecting the box jumps.
Also bare in mind most crossfit gyms are concrete covered by a thin horse stall mat but at least most crossfitters wear shoes though some may go barefoot or minimalist.
While I hate shoes, I've grown to disliking doing box jumps barefoot and the olympic lifts barefoot. Hell, I don't even like jumping down and landing off the rings or bars in a crossfit gym barefoot. Not really an issue in a gymnastics gym (which I'm barefoot most of the time).
Are these of any benefit to anyone besides those looking to compete in crossfit?
Not really unless done on a spring floor. While Coach Sommer likes to call these "Senders", they really are just a plyo bounding series for lower body power training. Little kids start doing this across the floor or up and down stacked panel mats (and sometimes punches across the floor are done in the warmup).
In general, these are somewhat difficult to do, especially when fatigue sets in but allow for a fast cycling. Establish a rhythm is important but again difficult when fatigue pops up.
As well, as can be seen by last years frequency of achilles blowouts during one of the qualifiers pairing box jumps and deadlifts; they are probably fairly dangerous.
Proper volume and programming of plyometrics using depth jumps and the like should be covered in Verkhoshansky's material.