Firstly, I am not an S61 qualified pilot, secondly, what follows does not pertain to the S61, so apologies if it contradicts those S61 percularities.
We need to discuss some issues raised above. "Efficiency" of the rotor system in these conditions should be related to lift v drag ratios, not other factors mentioned above. Drooping and increasing RRPM are merely ways of playing with the lift/drag ratios using the influence of V squared in the lift and drag formula.
Each helicopter will have a most efficient lift/drag rotor speed and angle of attack and the idea of every modern twin is to have that most efficient speed (NR in this case) occur immediately after an OEI event.
The other issue is that at the ideal lft/drag ratio, any further degradation in speed ( droop) will not have a linear effect, it has almost an exponential one. So if you are flying the rotor at exactly the best NR for max lift V drag and you accidentally have to pull a little more, you will be making drag increase at a vastly higher rate than lift increases. I other words, if you are already topping out the good engine when this occurs, it cannot overcome the rapid increase in drag and thus droop occurs. Quickly. As droop occurs, you will sink a bit more as there is now less V squared. As you sink, you apply more pitch and the cycle gets worse quickly.
Accordingly, it is smart modern practice to have the acft operate a little above the NR speed that would represent max efficiency for Lift v Drag. That way if you make a small correction you will droop initially to a better efficiency, not droop to an exponentially worsening one. Obviously if you keep pulling because the initial increase in efficiency did not get you out of jail, then you are back to the case of being susceptible to the exponential increase in drag. But at least you had an initial increase to help you fix your problem and stay away from the ground. If you automatically go to the best ratio, then from that point there is no margin for error and any slight error you do make will result in a quickly worsening situation.
B205s (UH-1H Hueys) for example fly generally at 100% which equates to 6600 RRPM, but the Australian Defence Force used to beep down to 6400 NR RRPM for limited power operations because the rotor is much more efficient in lift v drag at that speed. They had several significant (and fatal) accidents using this technique as any slight error requiring them to apply more collective at a critical point induced a further and accelerating rotor bleed if they were committed to having to retain pitch.
They altered the procedure to ban 6400 RRPM after some 20 years and retained 6600 for limited power operations. As a result, any slight error would result in a bleed toward 6400 but as the rotor was becoming more efficient with the bleed, lift was increasing a lot too, and the pilot could correct the error. At least initially - which is all you need. The result was no limited power accidents recorded since the change ( more than 10 years). It was not the only factor that changed, but I hope you can appreciate the point.
As a GENERAL rule, 100% NR is a little bit more than the modern twin needs for max lift drag efficiency thus providing us with a slight NR buffer to cope with our less than perfect reaction to an OEI situation. Well at least some of us who are not perfect anyway
Some twins even require NR to be increased above 100% for further buffer on efficiency such as the EC135, 145 and even the B412EP. That way if you have an OEI it goes back to about 100% NR which is about most efficient without you having to look inside and try beeping up initially.
Anyway - generalisations will always fail to explain specifics, so I know there will be a ton of replies detailing particular helicopters that behave very differently to the physics laws generalised above, but I hope I have give you a general explanation. And we have not touched upon the human factor part of this buffer and the "reasonable pilot" 2 second reaction for the certification of The OEI procedures.
Finally, the droop has NOTHING to do with LTE. There is a wealth of other threads dealing with this and it would just hijack this thread. LTA (running out of power pedal authority) - Yes. LTE - No.