Linear Power Supply?

So ask SOTA. The Regen just provides a clean sine wave, not device specific low ripple DC.

You have asked a very complex question, believe it or not. First, one can argue whether "noise" from a turntable motor power supply can even enter the signal pathway. The answer is it can enter by direct radiation of EMI and/or RFI from the PS itself or by retrograde conduction from the SMPS into the power cord into the AC supply which could then contaminate the PSs for your amplification gear, if all the gear shares the same AC source. But in your case, you are protected from the latter phenomenon by the fact that the outlets of your PS Audio power regenerator are isolated from one another. (I trust you do not plug anything else into the outlet that feeds the wall wart.) Distance is the best way to avoid contamination by radiated EMI and RFI, in this case, since it is not practical to add shielding to a wall wart. OK, then the next issue, I think, is that not all SMPS Wall Warts are created equal. Surely some are better engineered than others, and I would feel confident that SOTA used the brains of Bill Carlin, the Phoenix Eng designer, to qualify the existing wall wart. So, let’s assume you have a "good" SMPS wall wart. (The PS Audio regenerator makes it even better because it cleans up the AC going in, in case the filtering of the WW is marginal.) To answer your specific questions, the PS serves the Eclipse/Phoenix Engineering electronics; it does not directly serve the motor per se, and I would guess that if the current setup is giving you stable speed at "33.33" on your Roadrunner, I doubt you would see any change in function with a better LPS; nor would it seem to run "more precisely", whatever you meant by that. I also doubt there would be any change in "motor vibration" on any measurable level. However, the brain is a strange place, so you might "hear" a difference. I have been using an Eagle+RR to drive my Lenco motor, for a few years now. I am completely happy with it, and I am not even sure whether it is running off an SMPS or an LPS. If I wanted an LPS, I would find out what voltage and current output are needed and then build it myself.

Thanks @lewm . My Roadrunner shows me 33.333 + .003 in operation and occasionally shows dead on 33.333 for stretches. I wonder if an LPS would tighten this up any more, if it matters. My measured W/F via Analog Magik is .06, which may in my estimation get even better if I were to upgrade my VPI inverted bearing to a ceramic ball and matching thrust plate.

By more precisely I meant would the motor run at a given speed with less measurable variance.

I do have a question into SOTA so I’ll see what they come back with.

I see much discussion out there about using LPS but nothing concrete about direct TT benefit. I do want to have some details on this as I don’t want to rely on an emotional response of mine.

SMPS technology may he applied to a high end power supply. Iirc CS Port uses them ( although they are run by a retired industrial power supply engineer )...but in general it seems a decent LPS is the easiest way to get into a better quality PS.

Yes better PS make a difference to turntable motor systems. 

A linear power supply is extremely simple.  It uses a transformer, diodes and capacitors and regulators to create a DC output from the incoming AC.

It's the oldest type of such converters and is in most high end audio gear.

A switch mode power supply is more complicated, much higher efficiency, much smaller, lighter and noise can really vary based on design.  Done well it's noise can be equal to or better than the best linear supplies.  Most are not done well. :)