If not signal purity what is the goal? Putting aside the perfectly reasonable 'listening enjoyment' or 'to see if it could be built', there must be some objective goal when designing and piecing together a setup?
I agree with you that signal purity is certainly one of the main goals of constructing an audio chain, but (as Bccc1 noted) not everyone necessarily agrees. I'll make three related observations to better explain why I offered the caveat above:
1) There are other kinds of "audio purity" that aren't conventionally thought of as distortion. What I meant by distortion above was total harmonic distortion (not necessarily other types of audio inaccuracies not commonly called distortion). A great example is time decay (usually expressed in a waterfall plot). A speaker may be able to reproduce a signal perfectly (i.e. with very, very low harmonic distortion, intermod, phase distortion, you name it), but after the initial impulse the speaker takes some time to
stop making noise. That kind of delayed spectral decay can cause music to sound smeared or indistinct, or if certain frequencies take much longer to decay than others it can make a speaker sound "boomy." This is related to phase distortion (because both are in the time domain), but they are distinct issues and most people don't refer to time decay as "distortion." Similarly, deviations or ripples in frequency response aren't customarily called distortion, but represent an inaccuracy in reproduction. But if you take "distortion" broadly as including all deviation from the original signal however measured, certainly that's one of the most important system goals. A better term for the overall bucket might be accuracy.
2) Also absolute lowest distortion (in the broad sense of total accuracy) is never the only goal in setting up an audio chain even for folks who are objectively minded like you and I. Other perfectly objective goals could include: 1) acceptable cost, 2) fits in my home, 3) plays loud enough for my needs, 4) durability, and 5) will not cause my wife to divorce me. You can always think of another way to lower distortion (unless you're the proud owner of kit that holds the world record for lowest distortion), but ultimately, even objectively minded folks have to keep their other goals in mind. I agree that in an unconstrained environment signal purity is the goal, but in the real world it will always be "as much signal purity as I can afford," etc. Creating the type of system I was talking about above (large drivers with high sensitivity and high power handling) tends to be expensive in both dollars and space, so that may not be a realistic option for many folks. Similarly Electrostatics and Magneplanars are awesome speakers, but are (comparatively) expensive, large, and power hungry, and electrostatics in particular can be quite fragile.
3) Lots of people don't agree with the premise that accuracy is the goal. Euphonic distortion introduced by tube amps, by vinyl, or even (to a certain extent) by speakers with paper/cardboard cones have made many people into devotees of those respective technologies even though they are necessarily higher distortion than other alternatives. Additionally, on a personal note, even though I'm a fairly dyed in the wool objectivist, I personally don't prefer a perfectly flat frequency response across the band. If I play back very high frequencies flat (above 10KHz), I find that it sounds very fatiguing and I eventually get headaches. I have a sensitivity to high frequencies I guess. But I deliberately introduce a roll-off up there (deliberately deviating from the accuracy my speakers are capable of delivering) because it sounds easier on the ears to me personally. Although at least one fairly famous mastering engineer (Bob Katz) has expressed that he introduces a slight roll off in the high frequencies himself, so I may not be too far off the beaten path.
I probably drifted way off the mark. My thought process was: A and B are simultaneously given current by the amp. B has 20x the mass of A. It seemed like it would take longer for B to start moving with respect to A. I'm happy most of my question made some sense.
You can measure how quickly speaker elements "ramp up" (it's called an impulse measurement). It's a complicated area, but the short answer is that the heavier speaker has a much, much larger "motor," so will not necessarily be slower to move (although some will be somewhat slower, depending on the design). This is actually one of the areas where bi-amping (doing the crossover before the amps, and not using a passive crossover) actually does help: when an amp is coupled directly to a speaker element it dramatically improves what's called the "damping factor" which is how quickly and effectively the amp can start and stop the motor. Again bi-amping has lots of benefits for system accuracy, just not many for what's classically referred to as distortion (at least in the speakers, as noted above it will reduce intermod in amplifiers).
More info if you're curious:
http://sound.westhost.com/bi-amp.htm