I don't see any reason to put in a burnout set in any program that is powerlifting related. Burning out is just that, burning yourself out and trying to catch up to recover for the next training day.
On another note I do find that I occasionally enjoy a good rep challenge with my training partners, just to do stupid things.
The last do stupid things day most of us were attempting a board press comp. We were doing 3 sets of 3brd, 2brd, 1brd, then back up again for three sets without stopping. We just kept upping the weight until we started dropping out.
We sometimes like to do deads for sets of 5 alternating sumo,conventional until we die. There is always the squat rep challenges as well.
Does nothing except kill us, but it is good fun at the end of a workout to just fool around and push each other.