I find this very interesting and relevant to the discussion of not only measurements, but verification of specifications and claims made by mfrs.
Any system with feedback will have a delay as it requires an error component to create a correction if the process variable (speed in this case) is not constant. The error term is usually run through a low pass filter to smooth the response, but even if it isn't, the inertia of the platter creates a time constant that cannot be eliminated, therefore any correction will take a finite amount of time to be effective. The control loop can be tuned to provide the best performance, but there will always be a trade off between fastest settling time and lowest noise. While the control loop can be tuned, it is constrained within a certain bandwidth dictated by the physical make up of the drive components: Platter inertia, motor torque, available power from the supply, encoder resolution and sampling time. To give an example, using a DSP based controller on a belt drive motor running at 600 RPM with a very low inertia rotor, the bandwidth is high and the control loop can eliminate speed variations in a 100µSec (10kHz) time frame, but this is not possible with a DD table with a heavy platter and a power supply with limited current capability.
It would be interesting if mfrs would give specifics about the control loop they use for a DD table ie: Loop bandwidth, settling time, % overshoot, sampling time, resolution etc., as well as the rationale for choosing the particular solution (lowest noise, best speed stability, most dynamic sound, etc.). While these specs would be difficult for the consumer to verify, reviewers could measure and verify and it does give the consumer a basis for comparison.
Some claims made by mfrs are easily verified or refuted. If a mfr says their DD table does not slow down with applied drag, it is easy to test for this by lightly touching the platter while playing a record and listening for a change in pitch. If the servo response time is too slow to compensate for such a slow pace test of drag (low loop BW), it also won't be able to respond to dynamic drag caused by variable groove modulation which occurs much more rapidly by definition. If a mfr is willing to stretch the truth on such an easily verifiable metric, I would be suspicious of other claims that could be more difficult to verify.
As far as lag time goes, it's a trade-off. By definition any feedback mechanism will have it. But, that doesn't mean all such are equal or that stable accuracy is thwarted by response time versus no feedback. You cited a DD with a heavy platter ... okay, use a lighter one. There aren't any inertialess tables, but a design that doesn't make use of inertia or count on it for stability may take a different approach. There are techniques for much finer grained encoder resolution and sampling time. Controller software can run on higher MIPS processors and be predictive based on available data. I disagree that slowing a platter with your finger is equivalent to groove modulation. (Was your example hypothetical or is there really a manufacturer that claims a table will not slow with applied drag?) I agree there are limits - physicality and its laws - but it is possible to shave response time finer and finer and I believe the results of doing so are audible.
I agree that more info on the control loop would be a good thing - it's near non-existent. Some manufacturer's (not necessarily table makers) don't want to talk with their customers or reviewers in technical terms. I've been discouraged from that in certain reviews - which I ignored. Others fear loss of proprietary technique, etc. Fewer technical specs mean less opportunity for confirmation, etc. It's also possible to give up specs as measurements without divulging implementation detail.