Couple of points, having dealt with TSO's and ANR headsets for over 5 years now:
1. TSO certification is about standardized production methods and meeting minimum performance standards. The "minimums" are very low, so attributing interference with window heat, poor audio quality or any other shortcoming to a headset not being TSO'd is really incorrect. There is no TSO testing to evaluate window heat interference with a headset. If there is interference, it is more likely an aircraft problem than a headset.
2. The only ANR headsets which could possibly block critical sounds in the cockpit are the Bose Aviation X, Lightspeed Zulu, and DC's modified with the ANR earpieces. They combine a hefty amount of passive with active noise attenuation. All the rest of the headsets, not an issue.
3. ANR technology uses microphones to compare and cancel noise. Most ANR is most effective against low frequency sounds, not higher frequencies, i.e., the human voice on up, wind noise and higher pitched audio warning tones. So, ANR headsets normally don't block human voice or audio warning tones, unless they are lower frequencies... except if the headset has tons of passive attentuation like the Bose X, Zulu or modified DC's.
Mike