In my early life, I did a fair few measurements on phono cartridges and turntables, and the main problem was always the quality of the test records.
Frequency response test records have a guaranteed performance lifetime of only 5 plays above 5kHz, after which the HF level isn't guaranteed any more due to wear. That's why frequency response LPs like the Decca have the same sweeps on both sides, to double the potential lifetime. Whether Decca were especially pessimistic I don't know, but other test LPs I had (professional ones, not the ones sold for enthusiasts to do their own tests like the Shure Audio Obstacle Course) were similarly restricted.
Tests for mistracking have a one-time use, as once an LP gets mistracked, the grooves are permanently damaged. That's why when I do mistracking tests, I stop the instant I hear/see mistracking, and move to a different part of the LP for each test, so that I don't mistake groove damage for mistracking.
Distortion, wow and flutter and rumble measurements all depend on how good the cutting and subsequent pressing are. Distortion depends on that introduced by the cutting lathe, and I've never seen any figures for how good that is. Wow and Flutter depends on the LP being perfectly concentric, as even a mm or so of eccentricity in the centre hole can result in more W&F than a good turntable produces. Rumble depends on cutting lathe rumble, and judging by the rumble on one or two of my 'silent groove' LPs, that's often much more than the turntable produces. The best (i.e. most consistent) way of measuring rumble is using a bridge device, but then the numbers that produces may not be comparable with the way the manufacturer specified their turntable.
As LP playback is not a mainstream quality medium....yes I know it can produce very satisfactory subjective results.......there's not much around in the way of new test LPs, old ones are of unknown quality so any measurements are suspect.
It should be possible, and I think it has been done, to use a vibrating platform to exercise the cartridge to get a frequency response and distortion measurement, and it could possibly also be used for mistracking, but I don't know of a commercial product like that. Of course this would test the phono cartridge only, and not the arm and turntable.
S.