haha,your like a pit bull i swear
the evidence is in performance in many rig's that ive built & listened to over the last 25 years,how damping factor relates to an amp being driven to it's limits is plainly heard as a loss of bass response in any true full range speaker system that can produce a full bass response.
control? protocol? dont be silly
when i can go to my closet & pull out 2 different 200 watt solid state amplifiers each with identical spec's except damping factor & 1 will give a great bass response at all levels while the other amp clearly loose's control of the bass what other spec is there to look at to determine why?
you asked"what does df have to do with driving an amp to it's limits",the answer is simple,people do actually listen to loud music on their system's & they also have the tendency to push their amplifier's & speaker's to their limit while listening,i know the cool answer from many people is that they never drive the crap out of their gear but that is not based on truth most of the time.
ever see a subwoofer amplifier with an extremely low damping factor? i never have.