Take the point about NR headsets, which I used from the early 1990s. Being short-haul, we had our headsets on nearly all the time. What I can tell you is that, when the cabin crew entered the cockpit, we had little difficulty hearing them and conversing. Admittedly, we often slid one earpiece off, but I'm not sure that was necessary. My understanding and experience was that it was steady "noise" that was almost eliminated: e.g., the 400Hz hum from the AC electrics, the airframe noise, and the engine noise.
I'd be surprised if "hot mikes" were phased out on UK-registered aircraft as a result of noise-reduction headsets.
There are two entirely different animals at play in commercial aviation boomsets and we need to careful that the features are not mixed up...
Active Noise Reducing (ANR) headsets (i..e. Bose Aviation X, Telex 850, etc) that include an electronic circuit to reduce noise heard when wearing the headset - what this system does is exactly as you describe - elimination of steady "noise" by comparing the noise signature outside of the earcups and generating an anti-phase version of the same noise within the earcup, resulting on cancellation of the external steady noise. This is an output system...
Noise cancelling microphones (or more accurately 'directional microphones') affect only the input signal (so heard in your transmissions, primarily to reduce noise in what 'you' send to others).
As for "hot mic" recording, I think there is a specific CVR configuration that allows hot mic continuous recording, but it does not seem to be standard.