I have always felt that the ANR's removed too much noise from the cockpit. They could conceivably mask the sounds of strange noises coming from the engine that would give advance warning of trouble.
ANR headsets won't mask "unusual" engine sounds by design. They simply send out an inverted sound to cancel out the one one coming from your engine.
You'll still hear everything, though not as loud. There may be some "optimization" done for regular continuous engine sounds, but that's about it, and wouldn't cover clicks, clanks and other glitches a faulty engine would give as early warning of an impending failure.
Plus if your model is anything like mine (DC 10-13X) there's an On/Off switch you can use in any doubt.
I don't quite get the part about sunglasses hurting. Are the arms too thick? If so, wouldn't that problem recur with any headset of a given shape?