The Rockport treatise should be compulsory reading for anyone either contemplating the design of a turntable or who is merely interested in this issue. I am not a designer of HiFi equipment but it is a compelling, albeit lengthy, read.
The most salient point of the white paper is the assertion that the turntable platform/motor unit is responsible for “50% of the music signal”.
Why is that? Well, if you display an audio signal on an oscilloscope you will see it presented in 2 axes. The “Y” axis represents amplitude i.e. signal magnitude (this is the cartridge's responsibility) and the “X” axis represents the timebase i.e. the “timeline” of the music (this is the turntable's responsibility).
The speed stability of the T/T is instrumental in holding up its half of the bargain by maintaining this relationship with the other half of the signal.
Achieving that target both in the broad and transient sense is easier said than done, as the white paper will explain.
As has been highlighted by various contributors in the posts above, parasitic vibrations related to the T/T can also affect the cartridge’s ability to perform its function thereby complicating the situation even further.
This is why T/T “motor units” always influence the final sound.
In the early 1970s, I think Linn were the first to make the assertion that motor units sound different and started doing AB comparisons with other turntables to reinforce this fact in the public mind.