I'm in the mood for getting more specific: you said there's no laws, only regression to the mean, but you haven't given any indication of where this 'mean' comes from in the first place. As it turns out, it doesn't come from nowhere. It's pretty well defined.
In quantum mechanics, things are indeed stochastic, and measurement results when taken in aggregate can be described as 'regressing to the mean', so the question I asked is, *what mean*? And in QM, the answer is, "the mean as described by the wave function". If the wave function of a quantum system gives us a probabilistic spread of possible measurements, then the "mean" being regressed to is the mean of that probabilistic spread.
And the wave function, in QM, it turns out is governed over time by the Schrodinger Equation - that equation defines how wave functions evolve over time.
So I think you're absolutely right in an important way, that we observer regularities because of a regression to the mean. I think you're stopping short when you don't ask yourself the question, "where does that mean come from? The mean as defined by what?"
So now we know where the mean comes from - the Schrodinger Equation, which evolves the wave function deterministically over time - what we have is something people might metaphorically refer to as a "law". However, this time it's not a law that's defining a singular behavior, it's a law defining statistical behavior, probability distributions. But a law nonetheless.
So even if the regularities we see are due to regression to the mean, when we look deeper into what that actually means, it looks like "laws" are still a pretty good metaphor.
So, the question here is, when I refer to the Schrodinger Equation as a law, am I making an ontological statement or just a statement about my model of the world? And I think my answer is, a little bit of both. It might be that hte Schrodinger equatiation and/or the wave functions are ontological, OR it may be that they're a model we have of something, and maybe our model is maybe a bit off, and maybe there's some other ontological reason why it seems like wave functions are obeying the schrodinger equation with remarkable consistnecy -- and it just turns out that hte schrodinger equation is a really good approximation of that ontological reason, or an approximation of a high-level consequence of the ontological reason.
But it would seem to me that, even if we're a little bit wrong, there's still *some underlying reason*. And I call that underlying reason a law.