It may have had more sense with pre-PRML drives, not on modern ones , in my opinion.
What's worst, the onboard regulation you're talking about is not very expensive albeit "decently" tight (the power supplies on PCs are usually crap so you can imagine what can happen).
Some times ago there were speculations about this kind of experiments , I made some research and found it almost useless (nothing changed dramatically, so you can't tell if it was weak head, ECC, temperature, or external factor) to vary +/- the supply voltage.
What I have noticed is that +5/+12 supply is not critical (although you have to remain in decent range) , BER changes if there is noise / HF noise superimposed but between a certain range nothing changes at user level otherwise few PCs would work , if you consider the quality of PS. If you have a DDA or a 1 - 2 GHz scope you can display the read channel, depending on the drive family you have to find a way to trigger the visualization (otherwise, capture and see it later).
Power cycling the drive is necessary when drive is not responding anymore, and it forces recalibration, re-read the service area and flush caching if not disabled, it has some beneficial effect in CERTAIN situations.
You can do some kind of action via SW, but the way to do it is brand/family dependent so a general solution is considered (power cycle).
Of course, in case of partial failure or on certain circumstances varying the power voltage "may" have some effect but it's an exception, not the rule.
Also, on modern drives, the decoding of data / servo etc. is done almost interely thru digital signal processing (SW) so the effect of mild power regulation is counterlimited.
Instead of playing with power, due to the design of modern drives, there are many other factors that can be "tweaked" or "played with" SUCCESSFULLY to squeeze some more data out of the drive.
Final consideration : due to the cheap design of drive electronics, it is not advisable to play with +5/+12 supply voltage beyond a certain SOA. I am quite sure a good % of drives are exposed "normally" to non safe power, so the failures and the wear out.
Why vary power has little effect :
1) if servo is locked it should stay locked.
2) the preamp is usually powered at negative voltage that is meant to stay constant (it is usually derived from a DC-DC converter or from a section of the motor control) and it will stay almost constant.
3) the parameters for preamp are set via SW and there is a certain amount of auto-tuning
4) all raw data that comes from the read channel is interpreted thru DSPing.
5) rotational speed will stay almost constant as there is usually a closed loop regulation either HW and SW controlled (BTW usually the VCM/spindle is powered thru the +12 line on 3,5")
7) due to the nature of encoding of data on surfaces, small variations have almost no effect (otherwise even the slightes vibration or problem could have catastrophical effects)

below a certain threshold, internal locks on R/W subsystem trigger to avoid corruption of data as the heads are always flying on surface. I don't want to know neither I want to try on live data what happens - for ONE brand I am sure that power failures lead to "zap" (magnetically) the surface or at least do servo damage.
9) below another threshold, the MCU is reset (POR triggers). During POR the entire drive is inoperational (this is for safety and to avoid malfunction).
Today must be one of the "pro bono days" I don't usually discuss...
And now I expect also this post to go somewhere else on other people's name
