Issues of voltage regulation arise from when a Class AB amplifier's power supply also powers the amplifier's Class A preamplifier. So running the preamplifier from the amplifier's power supply might not be the best situation if the amplifier's supply is insufficiently stiff.
Here's a handwavy explanation of how and why that happens. The truth is that I'm uncertain it matters in practice for "normal" volume levels, as once the amplifier falls off the distortion cliff it's all over, and finger pointing to which section contributed the worst of the distortion becomes pointless.
Class A
In Class A the load is very nearly constant — a first order approximation would say that it behaves as constant — so the passive (linear) voltage regulator — some variant of RC, LC, or LRC instead of active silicon — in the power supply may be far simpler, typically a few cascaded stages of LC filter to remove the majority of the ripple current and noise. A current reservoir — be it some combination of charge stored in capacitors or flux in inductors/chokes — is a needless expense since the load is not fluctuating. With steady state an adequate supply will always be adequate.
Because preamplifiers are Class A and low power, their voltage demands on the power supply are both constant and minimal, the greatest improvement arises in terms of reducing the ripple current and noise which may otherwise be amplified in the high-gain front-end and the subsequent cascade of gain stages.
Class AB
In a Class AB (or Class B for that matter) output stage which is reproducing fast-moving transients the current demands rapidly fluctuate.
A rapid response, in consequence, is required from the power supply to avoid voltage sag, or distortion results. So the power supply must be low impedance to be able to rapidly respond to fluctuating demand without degradation in the B+. (This requirement is true for tube amplifiers as well as solid state; it's all about reserve capacity for transients.) Either isolated RC stages or big chokes were added to serve as the current/charge reservoir, and the amplifier designer was limited in stiffening the supply by the considerable expense for the choke or filter capacitors.
In the old days voltage regulators required multiple tubes and were very, very expensive. I have a tube regulated power supply with no ripple which cost three times what the Dynaco ST-70 cost. Pricey. I will some day restore it as a curiosity to power my breadboard. Modern regulators are far, far superior as the regulator rapidly increases the voltage to prevent sag from current peaks, consequently appearing to the load as an ultra-low-impedance supply, unlike the multiple stages of RC filters which have a charging time and resistive losses.
Piggybacking Class A Preamplifier on Same Supply for Class B Output Stage
The problem arises when the preamplifier piggybacks on the B+ supply for the power amplifier, such that preamplifier and amplifier now use a single, identical source of B+.
In such circumstance any modulation of the B+ by the Class AB amplifier output stage will simultaneously modulate the supply for the preamplifier, even though it is Class A with a constant load. Think of this as the dog (Class AB output stage) wagging its tail (Class A preamplifier stage). Conversely, one could argue that the (tail) preamplifier increases demand for B+ and thereby correspondingly increases the risk of voltage sag during peaks for the (dog) amplifier. That would speak to an inadequately designed power supply; why provide a tap, if using it would (routinely or significantly) degrade the sound?
The fact is that integrated amplifiers typically used the same supply, with a dropping resistor — as per earlier discussions about the constant load of Class A nicely lending itself to a single resistor — for down-regulating the higher B+ used for the Class AB output section into a lower B+ for the preamplifier, and nobody worried about modulation of the preamplifier by the output stage. The designers might have added enough reserve capacity to generally prevent sag, so it would only be the greatest transients which would cause noticeable sag, and thus distortion in the output stage, which usually is minor for moderate listening levels.
Amplifier separates, such as Dynaco, Fisher, Interelectronics, etc. commonly used plugs and cables to power a physically separate preamplifier chassis from the Class AB output supply. Separate power supplies were available to use the preamplifier with other equipment lacking a power-supply tap for external devices. A separate preamplifier supply, of course, reduces the need to stiffen the amplifier supply to better deal with transients.
Conclusion
Having written all of that, in the external preamplifier or integrated tube amplifiers we commonly see, the fast-moving transients in the amplifier's output stage likely do not cause significant distortion in the preamplifier audible, at least above and beyond the distortion already arising in the output stage.
By that I am suggesting and speculating that at output levels sufficient to stress the supply the resulting distortion is so significant that it is difficult to say how much results from the modulation of the power supply affecting the preamplifier stage, versus how much is simply the output stage clipping, distorting, or otherwise failing, and the preamplifier stage coming along for the ride on that distortion rollercoaster.
So it is not entirely clear that any defect in the stiffness of the Internelectronics supply for transients would deleteriously affect the preamplifier stage, or, conversely, that the tiny draw from the preamplifier would rob the amplifier's output section of necessary current and thereby result in voltage sag.
Determining the effect would need some measurements, which would be interesting to see as it might reveal some fundamental truth. As the kids would say, UR PREAMPLIFIER POWER, UR DOIN' IT WRONG!!! Or, maybe we're all doing it correct. Absent hard data, who knows?