It depends on how it's designed I suppose. A regeneration system is a voltage amplifier, but filtering could be built in. The only thing you might "gain" is a more regulated input to the system, but most system have the regulation they require built into them.
Like everything else in audio, if the user can afford it and it sounds good to them then they should use it, and since all setups are different - even those using the same equipment - nothing is universal and some setups may require things others don't. I'm just speaking from the general perspective of audio equipment design.
Yeah, it depends.
Here's the thing: we do have customers that have issues with variable line voltage, crappy quality AC (more square than sine), DC on the line, etc. These are the kinds of problems that cause mechanical humming, buzzing, transformers running too hot, etc.
A regenerator would solve that 100%.
BUT.
If it's a regenerator using a conventional transformer and a linear supply, the hum and buzz caused by high line voltage or crappy AC quality simply moves to the transformer inside the regenerator. So you get a silent amp and a buzzy regenerator. Not ideal.
Or, if it's a regenerator using a switching supply, then the switching supply noise may be injected into the AC mains (or may not, depends really on the quality of the filtering.) So no hum/buzz anywhere, but maybe noisy AC. Not sure--we don't make these products and I haven't done any significant investigation into them.
What I do know is that everywhere we have high-frequency noise, like in our AC-powered DACs, we use an AC line filter. And the kind of noise the digital section of a DAC produces is orders of magnitude less than that produced by an off-line switcher.
And, it's important to note that a regenerator is much, much, much more crazy than an AC filter. A regenerator is literally a power amp that drives an AC power socket. It's almost exactly like making an audio power amp. It has some economies in that it can use slower/crappier output devices, and it doesn't have to perform except at a single low frequency, but it also has to swing a ton of volts (370V for 120VAC, about 3.5x the swing of a Vidar run single-ended, and multiply the swing by 2 for 240V). A power filter can be a simple and small thing like we have in our DACs, or the crazy 70-lb tuned LC resonant shunt filter that Dave makes.
Whether or not any of the above improves your system is, as usual, up to you.
So, as with everything, there are no easy answers.