ANR is not a bad thing. ANR is primarily for folks who don't want to wear muffs and plugs together. It's all part of a continuum of noise reduction options. From least effective to most effective:
1. Passive headset alone (assumes a high quality headset)
2. Earplugs alone (assumes a high quality, well fitted earplug)
3. ANR headset (assumes a high performance brand, i.e. Bose, Lightspeed, DC)
4. Passive headset with earplugs underneath
Not sure about ANR with plugs underneath. Current ANR engineering assumes an open ear canal. Has anyone tried that?
Make no mistake, there are blurry lines between all of those choices. Headsets, both passive and ANR, have better performance at low frequencies, earplugs at higher frequencies. Depending on your current state of hearing loss, the spectral content of the noise, and the psycho-acoustics associated with what types of noise bother you the most, your mileage may vary by quite a bit.
At the end of the day it's a trade off between performance, convenience, comfort and cost. Personally I bounce between options 2 and 3 listed above. On hot days I prefer to err on the side of light weight and thermal comfort (Clarity Aloft) vs. convenience, irritated ear canals, and ultimate noise attenuation (DC ONE-X). But I'm flying without a helmet and flying relatively quiet Robinson products. If I was in noisier territory, or required/desired to wear a helmet, CEPs under helmet muffs would likely be my choice.
Here's an interesting article on how ANR is quite obviously just another layer in the arsenal.