about the title. bass is low frequency so it's the slowest stuff by far that a driver will have to handle. so of course any concept of speed is irrelevant here. 100% of headphones are way way faster than the fastest stuff a bass requires. maybe you mean having a strong enough damping but that's a significantly different thing. TBH I suspect that the frequency response in the low end(if there is a bump, how and where the subs roll off), and the level of distortions are what form our impressions of "good" or "muddy", "uncontrolled", "slow" bass. speed is more of a subjective misuse of the objective concept that then turn out to be reasoned by people as what must be improved to get that feeling of "speed". an actual faster bass would just be a higher frequency.
about extrusion, it's not like with speakers, to the point that dynamic drivers in headphones typically don't bother with a "surround"(the stuff that suspends the cone to the speaker's body). instead the diaphragm is directly glued. that should tell you something about how much smaller the movement requirements really are on headphones. and of course they are, you don't have to reach high SPL in a big room at a distance, with headphone you have to reach the same SPL while sitting right on the ear in a tiny acoustic chamber.
about grabbing the air with little hands and pushing it a certain way instead of another making the sound of some design different than others, there is no simple answer because be it on the electrical, mechanical or acoustic side, everything interacts and influences everything else. some a lot, some not so much but you will rarely get any clear cut answer because you will almost never be able to only get one specific change affecting only one other thing. therefore deciding that a certain impression is caused by a specific change is not as easy as many audiophile like to make it seem.
a simple example would be the fact that with a headphone we have a mix of sound wave traveling in the air, and the sort of pumping action. we're certainly getting traveling sound waves, but at the same time, just let a little space between your head and the pads and the amplitude in the subs will usually collapse by several dB. different designs and sizes will impact how much low end you lose when doing so, but they don't really tell you anything about bass quality(subjective or objective) while you wear your headphone properly. it's just the use of different designs leading to sometimes different, sometime pretty similar results.
as to your point about IEMs, I believe that you're wrong. I most certainly don't feel the bass I can feel with a full size headphone, just like a headphone never comes close to speakers despite how said speakers will often roll off in the subs a lot more than the headphone. and my hypothesis on this is that it could be a matter of physical shaking instead of actual sound at the eardrum. an IEM is so small so light, with such a tiny mechanical power that shaking anything is a challenge. a headphone might, depending on the weight, clamping force, size of the driver, etc, give a physical shaking along with the sub sounds. even if it's limited to the head where the pads touch, or maybe a little on the skin in front of the driver? but it's believable IMO that we might at a certain output level feel that shaking and subjectively interpret it as "bass so stronk and real!". it can't challenge the feeling of the entire body shaking from a subwoofer, but it's something. and Floyd Toole explained that we do get influenced by physical vibrations, even when they don't come from where the sound source is, and even when the physical shaking is not at the same frequency, it can still improve our sense of bass. so it is my hypothesis for now that IEMs fail in that specific aspect, so maybe it's why some people are never satisfied with how the low end sounds on IEMs. except they're probably not actually complaining about sound, just can't define what is missing in their experience. which could explain why some will try to compensate by increasing the bass amplitude, or some may look for something that extends as low as possible while remaining "flat", despite again how their speaker counterpart probably don't. and some will simply never be able to fool themselves into feeling a "believable" music in the sub frequencies. different people will not be influenced as much by certain variables in the same way. I know many people who think the bass they get from their IEM is amazing and much better/cleaner than something a typical speaker would provide. I'm not one of those, but I kind of understand how they could feel that way, so long as they don't miss tactile bass too much(which I always do).
or maybe it's just that we are overly used to speakers and their levels of distortions and room reverb, so when we get subs with a different frequency response(fairly typical of ortho vs DD case), or a lot less distortions, or almost no reverb, then we don't recognize it as matching our idea/memory of proper bass? IDK.
subjectivity makes diagnostics really hard, and trying to tear down complicated models into single variables cause-consequence concepts usually just makes us reach fallacious conclusions because we rarely can actually test such ideal and simple models in real life to know if we're right or full of it.
I guess my main point is that I agree with the warning not to assume that speaker's know how will automatically translate as is for headphone.
