Direct Drive vs. Idler Drive vs. Belt drive

I'd like to know your thoughts on the strengths and weaknesses of each drive system. I can see that direct drive is more in vogue over the last few years but is it superior to the other drive systems? I've had first-hand experiences with two out of the three drive systems but looking to learn more.
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Some more detail on the Burmester 175.

"The drive is not only equipped with its own tonearm and MC system, but also with a first-class phono equalizer, which is even supposed to keep the legendary stand-alone component Burmester 100 at bay in some areas. The barely compact turntable may still be worth its price of 31,800 euros, but its fighting weight of 60 kilos is not. This classy lathe is incredibly heavy!"

They are not joking as regards the pricing, I say! 🤭
Some more if you please... 😉 

The fact that the housing of the new Burmester 175 record player “builds so high” has, of course, also very practical reasons, after all, the developers packed in some key features. Above all, four motors, which, according to the manufacturer, are in the outer square around the sub-plate. One speaks here of the squaring of the circle, and relies on several belts, so that no uneven pull on the central bearing can arise. A total of four belts are used here, two for two motors each, which, according to the manufacturer, improves the synchronization, but also shortens the start-up.

The AC synchronous motors used here are driven by digital motor electronics, based on a high-precision oscillator and a perfect sine voltage. According to Burmster Home Audio GmbH, the electronics here are designed so that they are completely immune to fluctuations in the mains voltage frequency.
La di da, 4 motors, 4 belts - is this because they can not build a DD table? — Or is it they think 4 belts are better than none? 🤔 
M. 🇿🇦 
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. 

An update to my last post. A point I didn't make clear. 
The change in angle between the  rotating field and the rotor due to dynamic changes in load is a momentary change in platter speed. It is measurable and audible. Over time the average speed does not change, so we would not see this effect with say the Timeline laser. This, because it only tells us if the average speed is correct. These multiple subtle speed changes go unnoticed when this type of  measurement is used. We need to use much higher levels of granularity to see them. 
Further we do not perceive them as actual speed changes. ("that piano decay is wavering") isn't a descriptor one would use for this effect. It is more along the lines of solidity. Can we imagine walking up to the sound and actually holding it. Does it have mass and texture. These features are negatively impacted by these micro speed deviations. 
An aside, the cartridge doesn't differentiate between a change in platter speed or a momentary change in platter/ arm position. Both actions will be interpreted as a speed changes. So we need to have brilliant bearings in the arm, we need to pay close attention to the paltter bearing, the mounting of the arm with respect to the platter and of course we need to carefully control any tendency for things to resonate. I think that the key imporvements we will see in future TT designs will be the holstic attention to this time domain parameter.