I agree with GreyZone. In 1956 Hubbert had a range of URR estimates based on his geologic analysis. It was his upper bound that actually turned out to be right for US production. If you haven't read the 1956 paper, do so. It is very interesting.

Hubbert presented the logistic equation later WHT and Deffeyes have documentation on it. I don't disagree with anything you just said. My understanding is the logistic curve was introduced by Hubbert. And yes like any curve fitting method you need at least some reason to thing the data and the model are in rough agreement.

The main point is that the focus should be on the dampening term and in cases where bot HL and shock apply its instructive to understand how the the real term and the empirical term happen to give the same answer.

Its easy enough to throw out HL just takes a small amount of work to correlate the two models. The reason this is important is we have used the empirical HL model a lot we need to show how we moved to a new model. And a bit on why the old one worked.

Its just curve fitting in one case we have a non-physical logistic curve that fits and a better model that fits the data. All you need to do is show the terms in the better model that correlate with the terms in the empirical model.
This can be done with simple parameter variations to show where and when the two models are close.

Another reason to do this is it gives us a better understanding of the physical dampening terms vs the term used in the logistic. Its hard to grok why the logistic one works. And its not obvious what the real term should be.