The problem is not the motor it self making noise.
This assuming the designer has used a good one. The problem is the interaction of the controller/ motor/ platter feed back loop.
IMO the designer should use what I call a very tight motor. I mentioned earlier the phase lag between the rotating filed and the rotor......
Imagine a clock with 2 second hands. One is driven by the motor the other is pulled along by the driven hand via a rubber band ( now where have we seen this before?) As load increases on the hand being pulled, it stretches the rubber band a little but still takes 60 seconds to complete a circle. Reduce the load and the gap between the two decreases, but again it still takes 60 seconds to complete a circle.
In a tight motor the rubber band is very stiff and it takes a lot of extra load to make it stretch further. In a loose motor the opposite is true, the hand can easily move about, increasing or decreasing the gap.
If we now apply feed back around these two types of motors we can see that we can be less precise with the loose motor as it will have a softer response to and input command. Whereas a tight motor will respond quickly feeding into the platter. This does not mean that the loose motor is a better choice, since,it will not control the platters speed as well. There is an unavoidable lag between command and response. What is does mean is we need to be very careful to finesse the feedback to a tight motor to give us good dynamic speed stability. If we don't we will induce noise into the platter as the motor rapidly responds to an excessively aggressive command.
And no, a high inertia platter won't save you, it just extends the time constant, meaning that it takes longer still to correct. The motor needs to be able to dominate the platter.
An iron fist in a velvet glove.
cheers.