I disagree. Any punch cocks the opposite arm for the next punch. As long as there is torso rotation and weight shift(& hips rotation that comes with it), it ain't an arm punch.
Arm punches relies more on your shoulders/arms for power, when you can put your hips in it for more power with less overall effort.
No reason for arm punches, even when throwing multiple jabs one can use the hips/weight shift+forward momentum.
I think there seems to be some sort of confusion between an "arm punch" and a feint. Right hand "set-up" for left hook, from described below is actually a right hand feint to set up left hook. Arm punching is not feinting, a feint is intended to actually "fake" the opponent into a reaction and "arm punching" is not to be confused with feinting. They are completely different techniques, and i agree with you that a feint is not an arm punch and to "sell the feint" you do want to use hip n shoulder rotation, since the idea of a "feint" is to make it look believable.
Of course your going to get more power by using rotational force from the larger muscles in your core (legs, hips, waist), and generating power is far more efficient by using the core and getting leverage into the shot.
Arm punching, as being described in this thread is really a tactic that is suited to fighting inside, while set in the pocket or with your opponent or yourself backed up to the ropes, basically arm punching is used most effectively (in my opinion) when stationary. Given a stationary opponent, arm punching or slapping and tapping with your punches helps you find openings by baiting your opponents reaction. I.E, slap short left to right hooks or Uc's at your opponents head or gloves to get your opponent to pull his guard up high, then drop down and unload one into his gut. Tapping or arm punching jabs/lead hooks can also be used inside in multiples to bait your right hand or lead hook, i.e: if there slapping or dropping the parry down low you can lead hook off the jab over top the parry.... or if there pulling their guard up and "ear-muffing" when you slap lead hooks, you can fire the right hand in between the guard..... etc..... either way, arm punching can and does have it's uses.
Also, arm punching does not necessarily have to mean there is not any incorporation of the hips or shoulders, at least by my interpretation and i think this is where some disagreement is being caused in the thread, I.E: Paul Williams or Nick Diaz. Instead, arm punching still has a certain level of hip and shoulder rotation but uses the arm to kinda whip or slap the punches into the target vs. rotating all the way through with the hips n shoulders and really driving the punch into the opponent with some "ass" in it. Hence, why "arm punching" is also sometimes referred to as "volume punching" or cumulative damage type punching. Yes, the hips and shoulders are still used, it is not 100% arm, but the hips n shoulders are used to start the momentum of the punch but then the arm is incorporated to finish the punch or slap/whip it into the target. The idea is that to really volume punch (like Diaz or Paul Williams) your not really setting your feet and driving through the shot with your core, allowing you to maintain mobility and keep actively striking or volume punching while still being very mobile. That type of volume punching is a form of "arm punching" and is a very effective method of punching. Some guys just use it occasionally to mix it in with their power punching, others like PW or Diaz use it much more consistently and actively, occasionally throwing in power shots.