Everything else we've ever observed has initially appeared to be random. There was a long slow process of proving individual bits weren't random and then a sudden jump in progress after several thousand years of recorded history when Newton and contempories showed it all to pseudorandom. That is to say, it was never obvious that the macro level was deterministic.
For a statistics perspective, given the youthful nature of Quantum Mechanics as a field it is more likely than not that we're observing a deterministic phenomenon from the wrong angle, so it appears random. This is because that is how first contact played out with pretty much everything else.
It's an interesting way to think about it, but I have to say that even after reading what you've typed I don't really see it. Although Newton and contemporaries had mathematical rigour, there always seemed to be order in the universe. If you push on a cart softly, it moves slowly. If you push on it hard, it moves quickly. In fact, Gallileo had to show that heavier things do not fall faster than light things as it was imagined to be. Never did we drop a ball and expect its speed to be random. Even the word "random" comes from the mid 1600s and it comes from the idea to run quickly (i.e. without paying attention to a purpose). I don't even think the concept of randomness as we see it was a concept long ago. Everything was either a result of something else, or pre-ordained. Things that you couldn't explain were "God's purpose". Something with no purpose and no mechanism would be pretty alien to early thinkers, I think.
For a statistics perspective, given the youthful nature of Quantum Mechanics as a field it is more likely than not that we're observing a deterministic phenomenon from the wrong angle, so it appears random. This is because that is how first contact played out with pretty much everything else.