The universe is indeed treated as being deterministic. It's called unitarity, which means that evolution is non-dissipative. In essence, that means that information is conserved, which has given rise to the black-hole information paradox. The mere fact that there is a black-hole information paradox is an indication that unitarity is taken seriously.

As for why the universe doesn't appear to be deterministic stems from the fact that measurements are “classical”. This simple statement can be unpacked in many ways, for example by invoking decoherence. From my perspective, it is not so much related to free will as it is to locality. Measurements are restricted to only local properties, which means the nonlocal properties of the quantum state are lost. This loss is nondeterministic. Moreover, there is nothing we can do about it.

I personally think that information loss is fundamental to any observer, because observers make measurements to update models of reality. Given the model is essentially localized, it must be associated with information loss. This probably comes down to information density. If the information density of the model is less than or equal to the information density of the local environment, then there will be information loss. Given our brains process using synapses and neurones, the information density will be proportional to the connectome measure. Whereas, the environmental information will be related to the density of atomic species (it’s actually the density of states, which is greater again), which will be far greater than the connectome density. In essence, if the model contains less information that the system being measured, information loss is inevitable.

Thus the universe may well be deterministic, but we can never perceive it as such because we are just a small part of it and cannot see it for what it is.

The really interesting thing about the universe being deterministic is that we can actually seek to understand it and make predictions, so it’s actually quite a useful property. We understand our limitations in the process of measurement, but can nevertheless use the determinism of quantum evolution to make useful predictions.

However, with a deterministic universe, free will may be an illusion. Although, the indeterminate nature of measurement means that we probably have an effective free will. I think this is like having your cake and eating it too. We get the essential benefits of a deterministic universe, which means it can be understood, but our spatially localised presence incurs indeterminacy, which may well underpin an effective free will.