Sorry guys, quoting Toole again ...
Fortunately the world has decided that omni woofers are to be the norm. Even most "full bandwidth" dipole speakers transition to monopole bass drivers. I think dipole subwoofers have joined the dodo bird, as they should. There are a couple of cardioid woofers out there somewhere I think.
It is a real world problem. Around 1990 I had my first interaction with noted subjectivist Harry Pearson (RIP) when I was to be called to help him with a problem. He had heard a speaker he thought he liked and wanted to review it. When he got the speakers he placed them in his carefully selected "reference" locations and seated in his "reference" seat something was wrong with the bass. The designer of the speaker was called to find out what was wrong. I was invited to join him in what was likely to be an interesting venture. We arrived at Harry's house in the AM, and without listening to a note of music, we got out a tape measure and a calculator. He looked on in stunned amazement. Then we asked if the problem was a deficiency of mid-bass. He said "yes, how did you know?". It turned out that his "reference" location was arrived at while listening to full bandwidth dipoles, and the speaker he was auditioning was a monopole. We moved both the speaker and his chair and all was well. Dipoles couple maximally at a pressure minimum/velocity maximum and monopoles couple maximally at pressure maxima/velocity minima. Dipoles have the additional complication of being vectored sound sources, meaning that the orientation relative to a room-mode null matters. Monopoles are not. There are good reasons to use monopole woofers and subs. He remained in a kind of trance, exclaiming that he had never experienced anything like that. For pure subjectivists science, even really basic science, is a great mystery and/or threat.
Any woofer or subwoofer I have ever encountered does not change its power response "vigorously" - they are minimum-phase systems that are quite well behaved. However, room modes/standing waves do change dramatically with location of the ears or mic. That is the problem to be addressed. Mode cancelling/attenuation using multiple subs greatly simplifies the situation, but only when the budget allows. Good news is that with multiple subs the total system efficiency rises, so they can be smaller subs.