I've used Izotope's declipper tool on a number of albums. I think it's a wild overstatement to say such tools always work and always - or even most of the time - produce audible improvements. But I do agree they work sometimes.
In my experience it produces one of three outcomes:
- The de-clipped material sounds markedly more dynamic and retains most or all of the impact and presence of the original;
- The de-clipped material sounds more or less the same, or perhaps marginally more laid back, than the original but is not really an improvement;
- The de-clipped material sounds more dynamic but unpleasant, with reduced bass and/or undesirable alterations in the perception of the mix.
I've also found a high degree of correlation between the above audible results and how you have to set the de-clipper and what the de-clipped waveform looks like.
With the 1st, successful scenario, you can set the de-clipping threshold fairly conservatively and the result is a much more natural looking waveform with more randomized peaks. In this case a good deal of the compression was done at the final mastering stage, when the mix down was subjected to overdone peak limiting. The de-clipper has restored those peaks and the core mix is not overly compressed, so the result is good.
With the 2nd, "doesn't really sound better than before" scenario, the resulting waveform looks like the buzzcut original, but with just a few random "hairs" (aka restored peaks) sticking out. In this case a lot of the compression was baked into the mix (or the final mastering used heavy conventional compression and not just peak limiting), and so the de-clipper can't substantively decompress the sound.
The 3rd, "sounds different but actually worse" scenario, it's a version of the 2nd scenario: You can achieve more peak restoration and a more natural waveform by "digging down deeper" into the waveform, aka setting the de-clipping threshold more aggressively so that it will restore peaks for lower-level parts of the signal. The problem there is that when you set the de-clipper more aggressively, you start to get a real frequency imbalance in terms of what is impacted by the de-clipper and what is not - because bass frequencies have so much more energy and contribute disproportionately to the overall digital volume of the waveform, overdone de-clipping will rob the music of bass slam and in some cases also some warmth. The result can be thin-sounding an unpleasant.
Bottom line IMHO is that some overly compressed masterings have a sweet spot where you can de-clip enough of the peaks to make a difference without negatively impacting the core frequency balance, while others do not have that sweet spot - there's too much compression baked into the mix and compression is too fundamental to the sound of the bass and percussion.