Awww, I wish I had spotted this discussion earlier.
I used to design and build my own speakers and subs. At some point I thought of the bipolar subwoofer approach (I am sure that I was not the first) and built a breadboard box to try it out. It was amazing! Plenty of nice deep bass in the room, but the sub cabinet was absolutely inert. Kind of freaky since most speaker cabinets have some level of vibration. It taught me that all of the cabinet vibes that I was used to were not from cabinet wall flexure, but from cabinet motion. Cool, but what are the benefits? Well, less energy loss is good. However we all have more amp power than we need, so not a big deal. Not shaking the mid and tweeter around is good. There is such a thing as doppler distortion. I have never tried measuring it. Just used the "less is better" approach. Besides, I always use subwoofers, which are decoupled from the other drivers. Then there is the re-emission of signal from the speaker cabinets that are shaking. Can't be good, but I do not know how much it is not good. Finally there is the transmission of vibration to room structure. For me this is the big issue. I hate when things vibrate. I just want sound, nothing else. This becomes a huge issue in a small room, or in a vehicle. I have tried various approaches for vehicle sound, and I like this one the best. I currently use an old sub by NHT (the W2, I think) in my truck system. No vibrations to cause buzzing, just nice deep low end. Not an ideal sub design, but I no longer have the time or tools to make cabinets, so that is what I must use for now.
btw, it is possible to shake a concrete slab under a house. I actually failed a water line when I got a bit overzealous with the volume control a few years back. These were big bass reflex subs downfiring. I built them for outdoor listening (design criteria was 120db at 18 hz) but had to try them indoors. I do not know how much was due to transmitted cabinet vibration and how much was due to air coupling. Either way, just coupling the subs to the concrete probably does not make the issues go away. All of my designs are now bipolar in the LF range.