Stiffness associated with “slow bass”?? Only if the driver is high mass to gain stiffness. Btw. Doped paper is quite stiff and relatively low mass...this a preferred choice for high sensitivity woofers. Carbon fiber based and foam core drivers are also light , stiff and if used properly not slow at all.
Stiffness in and of itself is just one desirable trait and and when done with structure rather than mass is more often than not yielding a fast sounding bass.
Yup.
And mass really isn't the enemy with low frequency reproduction anyways. At low frequencies the cone isn't moving that fast, relatively, and a lighter cone isn't accelerating any faster than a heavier cone if the motor is sized properly. A lighter cone does not result in faster, snappier, etc. bass! A lighter cone can result in distortions that make the bass sound a bit more bouncy, full or energetic though.
However, distortion does go down as the cone becomes stiffer, especially as the frequency decreases. For subwoofers especially, I'll take a heavier, stiffer cone with a large motor anyday.
As far as "slow" sounding bass, it's also a theory that it's a result of excessive inductance according to Acoustic Elegance and I can see that being the case when the woofer is used into the upper bass/lower midrange regions.
And I don't see any room for interpretation on the definition of "pistonic" when it comes to speaker drivers. It's a word used in science and engineering that has a VERY specific meaning, that of an idealized driver that doesn't flex or break up.