Relating to power storage within an amp if you’re voltage coming out of the outlet remain stable, even on very hot days, then I think the only concern is spikes in Power needs to handle Sonic changes therefore it would seem the capacitors within a well designed lamp can more than handle Power needs.
Therefore it would seem the needed power storage reserves of a power regenerator are unnecessary given a stable voltage supply.
This statement is false. A power conditioner is not an additional source of power reserve nor is that what they are for. Spikes are a minor thing that are easily dealt with- you con't need a conditioner for that. Things like sagging voltage and the 5th harmonic are not! You need active circuitry to perform this task properly. Elgar made a power conditioner decades ago that was capable of this (and also regulated line voltage without limiting current) but it was marketed to industrial and commercial applications, not high end audio. The PSAudio conditioner is capable of eliminating a 5th harmonic and to my knowledge is the only high end audio conditioner with this ability.
So you have two choices if you want to do conditioning properly: find an old Elgar and have it refurbished (FWIW if something like that were made today by a high end audio company it would easily be the same pricing as the PSAudio stuff) or get a PSAudio.