Physicists are asking the the same question with different phrasing. How and when does quantum physics transition to classical physics, as modified by general relativity? Quantum gravity is part of this question. A lot may depend on the correct interpretation of quantum physics, if one can be found. Right now, interpretation is a matter of preference with little testability.
The universe becomes more deterministic at the quantum/classical transition, but not beyond it. At the largest scale, the cosmic background radiation has a lot of randomness. Statistics is required to tease out the structure.
RE: Why is the universe increasingly predictable at larger scales?