Then again, maybe groups of people can be associated together, and a poor match is good enough given other clues.
So, much better to be safe than sorry.
I'm not sure if I had a particular good point to make, other than that blurring does remove information that cannot easily be reversed. You can probably make very convincing reconstructions, but they might not look like the original person.
diminished in power.
It's only gone if it goes below the quantization threshold. Depends on the filter.
If you remove high frequency details, you in effect remove distinguishing features. That it is possible to create an absolutely convincing high-detail image that if blurred, gives the same "original" blurred image doesn't mean you have the correct deblurred image.
With not too fancy methods, I'm pretty sure you can make a blurred image identify as any multiple people.
I don't think this is a controversial statement either. In any case, this is a tangential discussion, since blurring to hide identities is a flawed method to begin with. With video recording, tracking, grouped individuals, etc, I'm sure reconstruction with good databases of likely subjects can have some surprising accuracy. So, better to avoid it altogether.
That said, one image, sufficiently blurred with a proper low-pass filter (i.e not a softer gaussian type, but one that just removes frequency ranges altogether), will absolutely not contain information to identify someone. The information literally isn't there. A large number of people are an equally good match, and then no one is. But, since combined with other methods I mentioned, it's a bad idea, then, yes, it's a bad idea.