Crab, please note, that I do not want to contradict you now, but I have a "but". I am not sure, if I would react faster to the loss of engine noise. Especially with turbine helicopters where sometimes the gearbox is quite loud, too. And with all the noise attenuating headsets, a brain will just tune the rest out. That might be the reason, why most if not all turbine helicopters have engine out warnings in the form of lights and "Bitching Betty". I think, from a "attention getting" point of view, something that comes up suddenly, is much more efficient, than something that goes away. AFIAK, that is the reason, why modern cockpits are designed as dark cockpits.
Again, as far as I know, because I have not flown everything out there, but from my experience and what is written in the POH's of those ships, in a piston helicopter the first indication is a yaw, for turbine helicopters it's an engine out light and sound.
Having said that, I have to add a disclaimer. I todays training world, throttle chops are a big NO NO. Today you have to yell "engine failure" and let the student do his/her thing. I don't know if that is better, because now the student never gets to experience the clues. For a better training experience the instructor should have a switch to make the engine out warning go of. That could be helpful. And all helicopters should have an engine out indication. Also every Robinson, Schweizer, Enstrom and Cabri.
I get it, why throttle chops are not en vogue anymore. Engine failures are so far down the list of preferred methods of beding helicopters, the gain in additional safety is small compared to the risk of additional accidents in training. Am I happy with that? No, because there is a tendency to train pilots to autorotate only to runways, to get it out of the way. Am I in favour of the full down auto? Yes, but to make somebody proficient in it, you need a lot of training time you don't have. On balance I prefer to do a lot of power recoveries to various spots all over the country side. The military can train its pilots to the standard they want, unfortunately in the civilian world, we can not do that.