Turntable speed accuracy

In a way we should think different, because speed stability is one side, sound quality has absolutely nothing to do with it and a turntable which creates "something" is also a total different animal (Raul is absolutely right on that topic).
When you want speed stability, a direct drive has advantages because it always is in connection with the used voltage, it always correct its speed during play (accelerate-hold-reduce-accelerate-hold-reduce and so on).
Direct drives are good for those who believe, that this has something to do with superior sound quality. A listened to some really good designs and I know, this has absolutely no influence. A direct drive TT can sound thin, lifeless and boring. Maybe there are exceptions ...
A belt drive TT Designer has to solve some problems, see Belt quality for example. Most aren't even able to solve this properly, then we can't expect that those are able to design a proper speed control. and this story goes on and on.
When someone is reading this and has no time to read the former 3 sites
- go for any suspended Basis turntable with Basis Controller or Walker Controller
or
- ask Sorasound for an Amazon turntable, they have a Battery power supply.
That one is good.
- or SME 20/30

Others produce "something" what someone likes or not. Discussions about "this" are endless because one prefers black, white, heavy, expensive, rare, PRaT, catholic or islamic soundstage and so on. These "problems" were all solved years ago, unfortunately engineering is no longer part of High End Analog. It is replaced with "I like it". Analog is a following of steps done right.

Gosh, what is left to say or think after that?
I agree that direct-drive turntables can be highly "colored", in a bad way. I also completely disagree; speed stability is the sine qua non of a turntable, no matter the drive system. "Sound quality", if by that term you mean the degree to which the sound emanating from the speakers can be made to emulate "real life" does depend very much upon speed stability. From that comes rhythm. From rhythm comes verisimilitude, in part.

Sure, a tt with excellent speed stability can sound bad for other reasons.

Why is a battery power supply, per se, likely to be superior to all other approaches to power supply?

We have pretty good reports from TW Acustic owners, who have changed the standard PSU with battery motor control unit from Raven Black Night.

No variable ac line = no variation in motor control = better stability.
Problem for many dd turntables IMHO is the fact that the motor MUST control (by nature here ..) the platter very direct with minimum delay.
Thus the use of a heavy platter with high inertia is counterproductive to direct drive.
IMHO however, high mass platter made with some insight in energy transfer and damping have inevitable positive effect on analog reproduction.
A DD with high mass platter "looks" at a similar problem as a BD.
aBoth have a kind of "overhang" in their reaction between motor speed adjustment/correction and reaction by the platter.

To resolve this problem some BD makers use optical feedback - to measure the platter speed and adjust the motor speed "in time". I think the new "Micro Seiki" spaceship is equipped with such a speed management system.