it seems that it offers no protection for frequencies out with that band whether the battery is flat or not
No, that really isn't the case. No protection? The Bose uses a light pressure earcup which as a result provides less attenuation than a typical mid-priced (say, £300) passive headset. But it is still a normal headset. Have you ever worn one?
A good number of people (passengers) have worn them without realising there is an on-off switch. Occassional poor passenger briefing is to blame for that, and I have been guilty of it once or twice too. Yet they didn't realise there was anything untoward.
Most of the noise in a piston plane is low frequency, and I would guess there are components up to a few kHz. I have a spectrum analyser so could have a quick look. Most of the noise near the top of that would be wind noise. However a lot of wind noise has a low frequency component coming from the prop blade turbulence. The Bose takes that all out well, and even crappy passive attenuation is good at removing high frequency noise. HF noise is really easy to suppress, using simple mechanical means. With voice reproduction needing only up to about 2-3kHz (in this context; the telephone network only goes up to that anyway) one doesn't need to use ANR for HF attenuation; any old piece of foam around the ear does that nicely.
You people need to visit a headset shop that has an aircraft noise source. I believe Headset Services at Shoreham do that. They certainly used to c. 2000/1; I went through most of their headset range in an hour and two headsets stood out clearly: the Bose X (£800 then) and a £500 D/Clarke 10-13X or something like that. The D/C was a bit better on overall attenuation but had a much higher earcup pressure. All the others were poor in comparison.
There have been some newcomers since then, which I can't speak for.