Wow, it is amazing to see that there are people who live in a parallel universe that seem to have no similarity with the world I live in.
Is your ANR specific to your aircraft type? It is around 15 years since generic broadband ANR systems were rendered obsolescent by programmable ones.
I have no doubt that your world, tecumseh, appears as real to you as mine to me.
But, KayPam, rest assured, the non-programmable "generic broadband" 1,000 $ Bose A20 is the best ANR headset that any of the hundreds of private and commercial pilots I know (including myself) have ever had the privilege to own. It's works brilliantly, and certainly perfectly does the job of protecting your ears in even very noisy (e.g., helicopter) cockpits.
I am afraid, yours is broken though. Mine has no considerable white noise when switched on, even in a totally silent ambience. Any noise, be it just the avionics fans or gyros, will - while substantially muted by the ANR - mask any very low noise the active headset may generate.
All this seems to become completely irrelevant once the engines are running. Here it is all about how much of the annoying engine roar is filtered out, regardless of head position, or spectacles worn, how well you can still discern changes in relevant noise (e.g., warning horns, changes in engine note), and how clearly you hear the voices of other pax and ATC. In all this the Bose is "the boss".