OK..... A few things here. And from the perspective of one who has fiddled with the audio/radio hobby for now well over forty (40) years. So forgive me please if I ramble a bit on the pendantic side.
a) A line conditioner is a good thing whether your AC line is typically contaminated or not. It maintains a steady output voltage within a very wide range of input voltages.
b) It puts out a pure sine-wave at 60 hz (50 if in other zones). Not necessarily grid-tied (a few more $$ gets you that), but close enough that your on-board transformer will be happy.
c) It is generally very quiet in normal operation, not so much if your incoming power is very nasty. Few here in the US will ever notice, in other words (unless the newly empowered Russians get their way - as demonstrated in Vermont lately. This is not political - look it up).
d) It will protect your equipment against spikes, brown-outs and other artifacts far better than a mere surge protector. Or a V-A-T.
So, if you have one, keep it!
Now as to a Variable Auto-Transformers (!!ONLY!! General Radio and its heirs may call their devices "Variacs", please keep that in mind). They are mechanical devices that reduce/manage/increase incoming voltages by taking off a simple coil at varying points. And the output-to-input voltage variation *AND PROPORTION* is fixed by the position of the wiper on that coil. Loads can cause voltage sags if the incoming line is not of sufficient capacity to carry that load. If you are getting a small voltage drop, that is normal - VERY!~!~! small. 0.583 % is very, very small. Variable Auto-Transformers DO NOT have any voltage regulating capacity whatsoever.
And, cutting to the chase, why it is that I would prefer an audio-grade line conditioner over a V-A-T 100% of the time. If your local voltage varies, a V-A-T is useless as the output is a fixed proportion to the input. Today, you are OK at 123 V-in, to 118 V-out. Tomorrow at 128 V in, not so much unless you are constantly (hour-to-hour) checking. Hence a set-and-ignore range of 85 - 145V becomes quite desirable.
As to bucking transformers - they also have one singular virtue: They will _always_ drop the incoming voltage by a specific amount, and do not admit to adjustment on the fly. Still not as good as a line conditioner, but far, far better than a V-A-T.
So, as John Muir once stated: Come to terms with your ass, for it bears you!. Understand what each tool is for, use it for that purpose, and let other tools provide as necessary for other functions.