If moving mass doesn't affect a speaker, how come no matter what level of brakes you put on a 4000lb car, its still going to take at least 130 feet to stop it from 60mph? Now, you are going to say "that's what stronger motor force is for". Stronger motor force can help control the speaker better, true, at the sacrifice of sound quality (distortion introduced).
This is a point at which the car analogy breaks down. The stopping force of a car is determined by many factors that have no relation to a speaker. Tires used, road conditions, rotor diameter, the number of pistons per caliper, etc. Dont take the car analogy to the N'th degree.
For example, the force/mechanism that propels the speaker cone into motion, is the same one used to stop it. Going back to cars, imagine their brakes being the engine, you simply reverse direction of the driveshaft and viola, you are stopping, and then moving the other direction. This is how a speaker starts and stops, using the same mechanism. Obviously, a car works much differently. This is why the analogy fails so rapidly if you try to apply it too closely to speaker physics.
A stronger motor does not sacrifice SQ and introduce distortion. In fact, the stronger the motor, the more control over cone motion is has (starting AND stopping), so the less (BL) distortion it would produce.
There are other factors that come into account besides simple motor force however. Most notably being the BL curve of the speaker. It could have a massively strong motor, but if BL drops off rapidly due to the design of the motor (narrow magnetic field, short coil, etc), then SQ will suffer. Conversely, a motor with less BL force, but a more consistent BL curve, could end up outputting less distortion then the motor with a higher BL spec, depending on excursion.
Split gap, xbl^2, and the various methods JL uses on the W7, are known as BL optimized motor types. This means their design allows them to have a consistent motor force (BL) throughout its specified excursion limits (xmax). Why do companies go through the trouble of keeping their BL force consistent? Because BL distortion accounts for 70-80% of the audible distortion created by a speaker (not to be confused with signal distortion however). That is more evidence of the significant role motor force plays in cone control (and how little mms plays a role)
Sensitivity. Lets say you have a lightweight cone/suspension. The speaker should have a higher sensitivity. It will require a lighter motor to control this mass. The speaker should be able to reproduce more subtle tones, more accurately. For instance, high quality pro audio or home theater speakers will reproduce drum sounds, guitar or vocals with more accuracy than a typical car audio speaker.This is because the speakers are generally made from lighter materials, paper or wool cones, and generally have much lighter suspensions.
Less mass, or more motor force, both gets you to the same place... better cone control. But my point is, motor force plays a much larger role than mms.
The home audio drivers you are talking about that use lighter materials etc (because they aren't in a harsh environment like a car) are midrange, tweets, and (most common) "fullrange" drivers. But again, my comments on mms relate to subwoofers only. The W7, with its 'heavy' car audio inspired cone and suspension, are being used quite successfully in a home audio environment. So have other car audio inspired subs, like the maelstrom, avalanche, etc. And guess what you usually see in a car audio sub converted over to a high-end home audio setup... BL optimization.
Also worth noting, home audio speakers tend to have looser suspension, and higher sensitivity, because enclosure size is a smaller issue in home audio than car audio. Hoffman's Iron Law tells us: sensitivity, low frequency extension, small enclosure.... pick two. Since most subwoofer builders dont want to sacrifice LFE, sensitivity is generally the trade off between home and car audio. In car audio, we tend to use low efficiency subs, and pump mega watts through them, because we want to cram then into tiny boxes in our trunk.
There is certainly something to be said for lower mms subs, the IDMax is a good example of a sub designed to (pretty much) minimize moving mass. It has a light cone, loose suspension, and its relatively efficient. There aspects of speaker performance we rarely discuss here, like timbre. This is where mms plays a larger role, the subjective end of SQ. But in terms of simple distortion output, no, mms plays a very small role, and BL plays a MUCH larger one.
Hope that helps make more sense of the topic.