Do things naturally spread out randomly? Given the same hand reaching into the same lottery box, does some inherent law of the universe guarantee that the number drawn is totally unpredictable?
Given our predicament of having limited information, and limited capacity for understanding, I agree that statistical models are some of the best tools we have, and a very practical way of navigating the world. Many things are effectively random to us, after all. We cannot hope to comprehend every variable at play when all of the numbers cascaded into the bucket.
But how random is it really? The electrical signals firing in your brain are as random and quantum as we could possibly imagine, yet somehow, you experience a single continuous consciousness, waking up as yourself morning after morning. How could that be possible if cause-and-effect were superseded by some principle of inherent chaos? Do you propose this randomness is merely too subtle to detect? In that case, it would be unfalsifiable, leaving us forced to conclude that the hand always draws the same number.