I appreciate the robust discussion, but to answer the OP's original question:
YES, of course amplifier "speed" and "resolution" can be measured.
In fact, I'm surprised that nobody seems to know how, but I guess we're all here to learn.
Let's take the Parasound Halo JC-1 monoblock amplifier, for instance. According to
Stereophile, this amplifier was noted to have excellent "transient speed," which allowed it to have "smoother, more refined sound."
This is what the amplifier looks like (see photo below). As you can see, it is resting on the floor. Using a precision instrument, I was able to measure this amplifier's speed. Out of respect for forum members who are in the U.S. vs. other parts of the world, I will report it in both metric and imperial units.
After taking a series of measurements using a radar gun, I was able to determine that this amplifier's speed was:
Metric: 0.0 kph
Imperial: 0.0 mph
Note: this was consistent with my unblinded observation that the amplifier was at rest.
Once finished with the speed measurements, I proceeded to measure the amplifier's resolution.
But
full disclosure: I did read the Stereophile article beforehand, where it was mentioned that the amplifier had phenomenal "resolution of low-level detail." I admit that this may have resulted in bias when I determined the unit's resolution. The measurement was also performed unblinded.
Using proprietary calculations that are built into the software code of Adobe Photoshop, I was able to determine that the resolution of the Parasound amplifier you see above was:
500 x 299 pixels
Now I realize that this post will be extremely controversial. I know that I should have measured before reading the Stereophile article, and I should have worn a blindfold while taking these speed and resolution measurements. However, in the name of science, I believe that my measurement technique can be replicated by anyone who chooses to, and this will let us average our results together.
Moving forward, I hope that we now know that, in fact, amplifier speed AND resolution are measurable properties.