I'm actually a physicist, and I agree with your requirement of defensible reason being more important than quantitative, but there is, as a physicist, some wriggle room. It depends on the quality of the data and the stage of development of the theory. For example, in Verhulst's time, there was no data with which one could do a reliable study of the effect of starvation alone, as opposed to starvation and disease, or starvation and war, etc. So Verhulst chose to simply posit that population tended toward a saturation number that was a new parameter in the Malthus model. In the absense of any real data, this was little more than an intellectual place holder for the idea that this model can't possibly be complete.

Then a century later Hubbert needs a simple formula for a time dependent quantity that starts very small, grows to a peak and then declines, ultimately to zero. He sees that Verhulst equation meets his criteria and uses it.

The Gauss normal curve also meets these theoretical criteria. I tried Gauss curve when first learning about PO. It leads to very messy algebra. There was no theory that supported using Gauss in this situation. The central limit theorem applies to large numbers of statistically independent events. Since I didn't want to use Gauss because the algebra was messy, it was easy for me to convince myself that there were surely not a large number of independent events in this situation.

He, like a physicist, doesn't have to justify trying it. Using it only needs justification if it works, and then the justification is more a discussion of what work needs to be done to develop a proper theory. Among other things, one needs to develop a good procedure for selecting data.

Elsewhere in the discussion I've posted a comment about how troubling it is that Hubbert linearization requires that the Hubbert peak be symmetric.

I think that we may very well witness the post peak decline in real life before we have a adequate theory of how to predict it. What we have now is good enough for economic hand waving, but as soon as decline is real there will be rapid changes that will lead to big forced changes in human behavior.

The key point is to determine if the data set shows a steady linear progression with a P/Q intercept generally, but not always, the 5% to 10% range (there are some outliers, such as the North Sea, an exclusively offshore region with a rapid decline rate). That is how Khebab chose the green points.

We don't have that many large producing regions to study. We can say that our available case histories--Texas (total plot, pre-peak is noisy), the total Lower 48, Russia, Mexico, North Sea, Saudi Arabia etc.--broadly fit the HL model. These regions account for about half of the oil that has been produced to date worldwide.

Meanwhile, what I first warned about in January, 2006--based on a HL analysis of the top net oil exporters--is unfolding in front of our very eyes, an accelerating decline in net oil exports. In fact, based on the HL analysis of Russia, in January, 2006, I gave Russia another one to two years of rising production before they resumed their production decline, and while Saudi Arabia has shown a rebound in production, it is a near certainty that they will show three straight years of annual production below their 2005 annual rate, at about the same stage of depletion at which the prior swing producer, Texas, started declining (all based on HL).

Recent headline:

Declining Russian Oil Production Could Lead to $200 Oil and “Global Recession,” Says Deutsche Bank

You are exactly correct in your observations and the choice of the time interval for the fit is the weakness of this empirical approach.

A true estimate of the variance of the curve could be gleaned if you randomly chose x points prior to the peak, doing this several hundred times and getting an empirical confidence interval. Have you done this?

Yes, but I use a Bootstrap techniques instead in order to derive a confidence of interval which is very often quite large. For instance for Saudi Arabia: