I really must put this bullshit to bed.
Dynamic drivers have motor systems that couple to moving diaphragms. The motor is capable of exerting force proportional to input voltage and current drawn. The motor and diaphragm combined has mass. F = m*a. Therefore, more force or less mass means higher acceleration. All things being equal, a driver with half the moving mass or twice the motor strength will be capable of accelerating from rest twice as fast. Just as a car with twice the power or half the weight, assuming the chassis and transmission are up to the task, will accelerate twice as hard.
Consider then a 15" woofer and a 8" woofer. Let's assume they have the same motor system, and assume that the 15" woofer has 80g moving mass and the 8", 40g (which are typical). The 15" woofer will have a radiating area of 800 sqcm, whereas the 8" has 200 sqcm. To displace the same volume of air, and therefore create the same SPL, the 8" woofer will have to excurse 4 times the distance compared to the 15".
So while the 8" woofer is capable of accelerating (and stopping) twice as fast, it needs to cover four times the distance. Doubling the acceleration halves the time needed to cover the same distance, but in this case of four times the distance, the 8" woofer actually needs to have four times the acceleration to produce the same SPL.
The limits of acceleration in a dynamic driver dictates how high in the frequency range it can go. This limit is attributable to diaphragm rigidity, moving mass, motor strength and electrical inductance, to name the obvious. To all intents and purposes, the human ear will not hear the difference in acceleration between the 8" and 15" woofers when driven properly and within their operating envelopes.
To finish off with another motoring analogy, the 15" woofer is like a car and the 8" woofer is like a motorcycle. Imagine them zig-zagging through a set of chicanes, except that the motorcycle has to zig-zag four times the width than the car. At some speed, which equates to frequency, they will reach their limits. Whilst the motorcycle can accelerate faster, it won't be difficult to imagine that the car has the easier task with much shallower chicanes, and will in, in all probability, deliver a higher terminal speed.
That's also why bigger drivers tend to be more efficient.