It wasn't random, because there is a 95% R^2. This means 95% of the price is explained by this model. All the other factor are explaining 5%
The numbers don't tell anything by themselves
For instance, you can take an arbitrary set of random data and build a model (say, a polynomial function of high enough order) that would technically give you a 100% accuracy, at least as far as only the sample data points are considered. Then, on this account, you could go on to claim that the distribution is not random (following your logic here). But it would be a far cry from actually explaining anything in a meaningful way, let alone having any predictive power (the analogy of a random number generator seems appropriate here)
This is probably a borderline if not outright extreme example but it is still illustrative enough to show that numbers can be misleading as well as deceiving, and thus shouldn't be taken in isolation for drawing deductions and making inferences. You can arrive at very bizarre conclusions if you don't assess and keep in mind the nature of the subject matter. Put differently, statistical metrics are sufficient and unreservedly valid only in reference to truly random populations. With everything else, we should rather be concerned with looking for the underlying principles, drivers and forces, i.e. the actual mechanics of some phenomenon or process, and how things work internally
Mistaking correlation for causation has already become a cliché of sorts, but it is only a tip of the iceberg of the whole gamut of possible judgment errors we have to deal with and be aware of
I totally get your point.
But i guess the original S2F model has already well demonstrated it is not a well articulated fit of a random data point, as it it cointegrated (this is a statistical test) and parameters are well stable over time (running S2F over different data sets, taken from different halving cycles for example, yields to almost identical parameters and price predictions).
A lot of your points have been actually been raised in the past and discussed in the above thread.
I think it is useful to approach the topic with a grain of salt and in a "challenging" way, as you are doing (we already have religion where you need faith to believe, models are different).
So I am happy to discuss your questions, as answering might me help me find the flaw in this model. I would like to find it, as I find disturbing to have a BTC valuation in the millions in a couple of halving....this means something (the USD) has to break to be true. Otherwise it is the BTC that is going to break.