THE WALL---Why?

Sure - the need for a wall outlet direct connection for AC input and the need for storage capacitors for DC power in power amps are the same - very large instantaneous current demands for music's transients. AC power outlets can supply 10000A+ for very short periods, I doubt any power conditioner can match that #. Paul may try, but alas it would be grossly expensive to do so...

Preamps and other line-level devices do not have the very large current demands. This is due to the fact that impedance levels are much higher (100x or more) as well as signal size being lower (100x lower as a rule of thiumb).

enliten

AC power outlets can supply 10000A+ for very short periods

No way ... at least certainly not where I live. And I've measured it. Many people would be shocked to discover that their 200A service can't even deliver 125 amps. In fact, 200A service isn't designed to actually deliver 200A.

It is mostly the fact that power conditioners or whatever you want to call them have a maximum current capacity and amplifiers need a lot of current. Regenerative power supplies have rather severe limitations for maximum wattage and can be damaged.
 I use a Monster HTS3500 and find it sounds much better if I plug my amplifiers into it. It is very synergistic like power cords and is up to your own ears. Each device ought to have its own recommendations and parameters. Your results will absolutely vary.

I am one of those audiophiles who have gotten excellent results when using an over-speced PowerPlant to clean and buffer my wall current. I've tried it both ways, and I vote AMP plugged into the regenerator. (By over-speced I mean my equipment draw is a max of 750va while the power plant can deliver 1500va, so I have 50% headroom.)