That's exactly how that plays out with the more crude simple noise reduction, Reason.
Here's something to consider. If you end up with an artifact from the nr attempt like the breathing thing or the popular wind chimes effect, you just ADDED noise to the recording that wasn't ever there before! That would be a fail if the goal was to remove noise, right? If you also lost some program content in that attempt - that's even worse!
It's tough when the noise is monumentally louder than the program. You really don't want to hit people over the head with a noise blast and talk of losing subtle elements of fidelity with that going on can seem ridiculous. Truncating the entire high end is looking pretty good sometimes...