Just to get a bit more technical, as this subject intrigues me, the power must also be related to the way the air flows. The intake consists of a number of pulses of air being sucked in by each cyclinder, so there is a lot of stop/start air flow. It would seem to be a good idea to reduce the stop/start, ideally to make it continuous. Air has inertia, so takes time (and energy, as supplied by the pistons sucking it in) to get up to speed, and the fuel injectors/air intake must work best at an optimium air flow.
So, opening up the air intake may make the pulses more stop/start, so less power ??
My supercharger puts the air through the same size plumbing as normal, but, because it is being pushed, there is less air inertia to be overcome ? Also, of course, more air in general, so the flow must be smothed out.