My point is more that, even when you know the underlying mechanisms perfectly and with infinite precision, there are systems for which you can't make any statis

My point is more that, even when you know the underlying mechanisms perfectly and with infinite precision, there are systems for which you can't make any statistical claims about its behavior. Even the Game of Life can encode a Turing machine, which makes its medium-term evolution impossible to predict ahead of time. That doesn't mean there's anything we are missing in our understanding of the rules of the Game of Life. Emergent behavior can be totally opaque, even when we have perfect understanding of the elements of the system. Just because the behavior is totally inscrutable doesn't mean there's anything we are missing about the underlying mechanisms. There's no hidden principle of Turing machines that would let us predict them reliably either- their underlying mechanisms are totally understood, the behavior is still essentially unknowable. Perhaps living systems are like that. It seems quite likely, since their underlying mechanisms are actually much more complicated than toy models like the Game of Life, that they can manifest totally opaque behavior without requiring any new physics at all.