I agree with @rvietor here — I think this assumption is false.
There was a recent discussion in another topic, I will just link what I wrote instead of repeating it here:
TL;DR:
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all mapping is about distributing (global) contrast, of which there is a finite amount.
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bring everything to the relevant tonal range before global tone mapping. trying to fix things at that stage is a futile exercise.
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consider sigmoid.
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