My new coach strongly emphasizes power generation through hip rotation as I punch. He also strongly disagreed with slugging from the upper body. For example: I push off the rear leg when throwing a cross. But, the power does not stream straight into my right arm. Rather, it hits my right hip, thrusting it into a pivot. Theoretically, that would throw my body weight behind my punch. Jab-cross-jab, for example, would involve me twisting thrice, very quickly. Is this a waste of energy? How else should I generate power? Sorry, if I wasn't being clear enough!
The punch starts from the gound up. To maximize the power you generate, your whole body should work together. Starting from the foot (pivoting is crucial), leg, waist (often neglected), torso, shoulder, arm, then fist.
Power starts at the feet and work it's way up the body to the fist. The fist just delivers the message but the message is incomplete if not delivered correctly. Everything about power generation matters. Generally it is the trunk rotation that generates the power. You can pivot less but still turn with your hips and generate alot of power. If you pivot, don't turn with your hips then you can't generate much power.