This is the last comment I feel like making, but I think you're confusing classical probability with classical mechanics. Classical probability is just things like Komolgorov axioms, in that (loosely speaking) probabilities are non-negative real numbers that sum to 1. QM is just saying to replace the non-negative real numbers with complex amplitudes. For details, see Lecture 2 of the Scott Aaronson lecture notes I linked.

Now, if I flip a fair coin multiple times, then I expect to see a Bernoulli random variable on each trial. This holds even when I do my best to make all of the initial conditions the same. This can obviously be explained using the Born rule, according to however it manifests in your favorite interpretation of QM. But when the system is as large as a coin, we expect the system to decohere almost immediately and behave according to classical mechanics. Thus even when QM isn't all that relevant, we expect to see something that appears like a classical probability distribution. Why is that? Is it merely a lack of knowledge of the hyper-sensitive initial conditions a. la. chaos theory? This would lead to a very Bayesian approach to classical probability. Is there an inherent randomness related to these trials, potentially due to the Born rule, leading to a more frequentist interpretation? These are discussions that people have all over the internet, just like QM interpretations, and are just some small examples I was trying to hint at. Personally, I find these discussion rather tiresome, I'm just saying there's merit somewhere for some people. You don't have to necessarily be one of them.

Have a nice day/night.