The weight of each composite on a 6.5" speaker will be lesser compared to 12" counterpart. It is very well known that a smaller speaker with identical composite will retract faster than a bigger one due to savings in weight. That's the physics behind it.
Let's define weight. It's a :force: that results from mass and acceleration.
A larger object, like a 12" cone, will likely (though not necessarily) have more moving mass.
But where you've made a mistaken assumption, is to assume that the motor is not scaled proportionally. A 12" driver is not being driven off the same motor as a 6.5" driver. The acceleration is higher, therefore the force being applied to air, is higher, and the reverse acceleration being applied to stop the driver, is also higher.
You also mentioned earlier that low frequency extension is a function of fs. To an extent, you are correct, because a lower fs will improve efficiency as frequency drops.
Now what has a lower fs? Hint: a "heavier" driver.
Where do large drivers have issues?
-suspension resonances as frequency rises
-inductance from large voice coils reducing efficiency as frequency rises
-cone damping / breakup modes
-narrowing off axis response as frequency rises
but sheer "speed" is not one of them. Something like the acoustic elegance TD15M, with its ridiculously low inductance, cloth surround, treated pulp cone, can reproduce frequencies higher than 4khz on axis cleanly at ridiculous SPLs.
If you put three 6.5" speakers, each one will still respond faster than a single 12" which will result in a better sound.
Now let's define "fast". "Speed" is measured in "per second"
Now let's examine the passband of a driver IE 30hz to 300hz
if 600hz is the highest frequency being asked from the driver to reproduce, that's 600cycles per second. See the correlation with "fast"?
Now if the driver has no issue reproducing 600hz, then who cares if a smaller driver is "faster" (IE the ability to reproduce 20khz or not)? it's INCONSEQUENTIAL.
Now you're confusing "speed" (which functionally is UNDESIRABLE as frequency drops) with "bass tightness". Bass tightness is not about "speed". The factors that presumably contribute to perceived sound quality include decay (room related), group delay (tuning related), distortion (driver motor related, and proportional to excursion), damping (Q related), and raw frequency response (room/tuning related).
There is nothing superior in bass about a 6.5" driver with respect to bass. If anything, it will end up being tuned too high as a subwoofer (high group delay), be equally prone to room mode issues, lack bottom end efficiency (some might perceive this as sounding punchier but it only means an unflat frequency response over the audible range), and require much more excursion to reproduce a given SPL at low frequency as a result of its small effective piston area (higher distortion).
But common sense is to be used here. Don't take it to extremism ofcourse 1" tweeter cannnot be used because they don't respond to lower frequency at all and the reason for that is because their XMax is severely limited to move any reasonable amount of air molecules. Hope that adds to the clarification.
That's not true either. low x-max does not prescribe "not responding" to lower frequencies - a driver can be high x-max and low fs as long as it's designed to work in a larger enclosure - some infinite baffle drivers are like this.