Yea that makes sense trying to catch a guy would tire you out, but if you didn't chase a guy wouldn't he lose points for not engaging you? But it seems everyone is just talking about the mainstay of power for a punch generating from your hips. I agree a bit comes from your arms. Bruce Lee worked out his forearms an amazing amount because he thought it made his punches stronger (from a Muscle and Fitness article) but I think you would be hard pressed to find good supporting evidence to prove that power (KO power that is) comes from your arms. I am with you that little nat like annoying punches you use when a guy is not actively trying to exchange with you don't come from your hips but I don't think thats what people are talking about. Oh, thats pretty tight you used to a be a game boxer man, congrats!
I heartily accept the motto, "That government is best which governs least"; and I should like to see it acted up to more rapidly and systematically.