A good way to objectively literally see that bass transients have tactile directional force, is the empty coke can on a table test.
Depending on displacement of the sub, the distance can be anywhere from 2-5m. An important factor is to have sufficient rear, and side wall clearance, so that virtual subs are not being formed.
A big bass drop or hard kick, can/will blow the can straight away from a single sub, on axis.
If the can is in between a stereo triangle, using the same transient stimulus at the same SPL at can, i've watched the can move unpredictably, wonkily, maybe back some, but most often as much sideways as back.
Adding a sub in the rear of the room, going MSO etc,.... makes the can want to vibrate in place....and erratically hover around some..
In addition to my post #98, IME it's not just about subs, although it highly depends on what job you give to them and some important qualities required. I'm sure you know what I'm talking about, i.e. some shortcomings of commercial subs that are of poor quality. And it's about the mains also.
As an analogy to an empty can test you describe, in attachment you may find a (very poor quality), but importantly a real time recording of some transients and what goes on about vector gravitational components of a device placed on a hard surface, about 3,5 meters away.
Sadly the device is unable to capture audio at low frequencies (100Hz is already severely rolled off) and there's some latency in processing and rendering the data. Just another inconvenience, devices mic is only couple of mm away from the surface it's sitting in, so it captures mostly the reflections off it, also distorts audio because of the force. Video is 60 fps. But still, this gives a better audio/visual clue than, for example, if I were to mix in the original audio track.
The track is this one:
As you may notice, it contains both quick bass drops and quite low frequencies, but it's not about stereo bass for this purpose. I didn't look into it, but I suspect it's mono bass most of the time.
From what I can observe, the energy is almost instantaneous because of high sound propagation velocity trough hard surfaces. But what sets things in motion is physics of high/low air pressure, acceleration, velocity and displacement, complex phase relations and acoustic impedance mismatch between air and solids. This is highly complex as the room is being the part of the system, so good luck in trying to model this...
So yes, bass energy can have a direction even in a room. In this case, device is placed upright, oriented left to right and turned towards the system laterally (arrow to the right means the device is being pushed away). Note that the low frequencies, even though not recorded, are also absorbed in a timely manner, not letting it flapping about. Regarding your observation, empty can I suppose on a capable system could be pushed away with enough force to be tilted out of balance, not being able to return to it's equilibrium state.
Important thing to consider is that the setup must be such that the energy is distributed in a controlled manner and absorbed rather quickly. Indeed the device shows complex gravity vectors acting like a shock absorber on a bumpy road. However, room modes (if they are supported) want to do exactly the opposite, i.e. behave like a ride with broken shock absorbers. Surely someone had experienced that.
IMHO, the key is in having net displacement (ports in room are kind of messing this up) as shown in a room gain analysis by
@René - Acculution.com . Also, for audibility of stereo bass I think vertical plane must be considered and it's a better job for the mains, rather than the subs. Subs on the other hand have a job of not smearing it up. But to set things up in a remotely practical manner, one may have to start from scratch. Because of that, I would think one should first experience this and then decide if it's worth the trouble, or cost, for that matter.
EDIT: Note -
Audio in attachment is quite compressed and loud!