my information comes from the past where I come from. In the 1960s and 70s, bass reflex port design (which had only just bugun to be understood) was tuned toward out-of-phase tuning to accomplish the taming of the resonant frequeny hump in the frequency response, and the audiophile goal was generally regarded as recreating the classical music concert hall experience in your living room without sound coloration, and which music does not have boom-boom elements, except for the occasional timpani thump. The subwoofer had not even been invented yet.
as to the efficiency claims, see the cousin-to-this-comment i just made. In brief, wikipedia is talking about comparing different designs, and I (and the original youtube video) were talking about the efficiency effect it would have on the self-same system, not compared to other different systems. You can surely see that out-of-phase resonance might be likely to decrease the sound level, and in-phase reinforcement would be likely to increase the sound level. That is what I was talking about.
(it's not actually as simple as what it seems on its face, the acoustic feedback of the sound waves (bass reflex) will be transmitted back through the electronics to the feedback loop in the amplifier itself. Think of it like a conservation of energy type argument, shifting gears on your bicycle does not give you more energy but it can increase the efficiency-kind-of-sort-of of the transfer of energy from you to your bicycle, so comparatively speaking shifting gears on your speaker. I say kind-of-sort-of because what energy gets wasted where (in the form of wasteful heat) isn't completely intuitive. systems have their lowest impedance at their resonant frequency, thus highest energy transfer, but feeding back to change the behavior at the resonant frequency will change the impedance rather than simply "hey free efficiency" or something, because we are changing frequency dependent impedance rather than removing resistance/friction.)
the musical problem with choosing a "resonance reinforcement" technique is that it works at the same resonant frequency all the time (same for that speaker, different for other speakers). What's pleasing about music is the artists choices of musical notes. Different songs have different note choices, but the speaker's resonant frequency is always the same so a song in the key of, e.g., G will always be emphasized in the key of C which does not make musical sense.
the opposite is not the case, if you use bass reflex to demphasize the resonant frequency, you are making all songs sound better.
in the particular case of the youtube video, he would still be wrong because he is measuring/testing right at the bass port, which for bass notes with a long enough wavelength would still be reinforced by the sounds from the front of the speaker, but not in the directed way that he is trying to capture with the smoke ring cannon because the reinforcing waves would be arriving from elsewhere and not coherent with the (hypothetical) smoke rings. also the smoke ring cannon is tuned for a much lower bass note, if you pumped 20Hz through it (an extremely low note, the limit of human hearing), that would imply 20 smoke rings a second. Does anything about the smoke ring cannon seem to indicate that it could put out 20 smoke rings a second? highly doubtful, they would interfere with each other. notice that the bass port is much smaller than the smoke ring cannon, probably a bad impedance match, though I doubt the smoke ring cannon is operating at all on frequency, just simply the turbulent movent of air (and smoke)