With all due respect, keve, I think that you are putting the cart before the horse. Before one aggregates observations, one must make observations. The difficulty with making speed observations is that for practical purposes they must be averages: distance travelled divided by elapsed time. This is not an instantaneous quantity.
Even aggregating a finite number of observations implies discrete, not continuous. That means sampling frequency.
This is not a moot point because modern controllers tend to correct speed at about 10KHz. If it were easy, they would correct more frequently. I doubt that an app is better; in any case, it's important to quantify the limitations of the observations; in this case the granularity imposed by sampling frequency.
Then one could aggregate the data into moments, from which the central moments of mean, standard deviation, skewness, kurtosis, etc. could be calculated, although perhaps a spectral or Fourier analysis would be more revealing.
There is no problem with the data arising from a process which is not perfectly random - it is data. The point at which randomness enters the picture is in identifying which inferences are valid, and which are not.
Yes, I think that speed stability is a problem. The question then is, "Which frequency?" I strongly suspect that most of the audible differences between turntables arise from small speed variations in the lower kilohertz range, which we hear as brilliance or sibilance. It is obvious to suspect speed instability of causing this - but at greater frequencies than are usually measured. For example, bearing noise affecting speed.
By way of evidence, a common criticism of Nottingham turntables (high mass, low torque) is that they are 'dark', that is, without brilliance. I prefer the term 'smooth'. Also, that is how the bearing noise from my 1.8W motor manifests itself. Yes, it's repeatable.
As you point out, "Measuring performance parameters of instruments is crucial to product development." But unfortunately, associating numbers to phenomena is one of the most difficult human activities - doing it right, that is. It is therefore of cardinal importance to report the limitations of the measurement before reporting the results of the analysis. In my opinion.