Checking other versions of the postultes, I find:
Sometimes it is stated for a single particle, but it cannot be true if the particle is entangled with another. Sometimes it is stated for scalar wave functions, but that cannot be true if the particle has spin.
You can correct those problems by introducing spinor-valued wave functions of several variables, but then you are still ignoring quantum fields and all sorts of other complexities.
Now you might say: Okay, but if use the whole Standard Model, or some bigger unified field that takes into account all possible interactions, and then we construct a wave function of the universe, then that would completely describe the state of the universe.
That would not be quantum mechanics. That would be some theorist's fantasy that has never been carried out.
Quantum mechanics is a theory that takes in some available info, and makes some predictions, but never achieves a complete description of the system. Nobody has any idea how any such complete description would ever be accomplished.
Take a simple example, the Schroedinger Cat. The wavefunction is a superposition of dead and alive states. Is it a complete description of the state of the system? No, of course not. The cat is either dead or alive. You can get a more complete description by opening the door and looking to see if the cat is dead. The wavefunction is most emphatically not giving a complete description.
I don't know why anyone would say that the wavefunction is a complete description of the system. Other physics theories do not start off with a postulate declaring some sort of god-like omniscient. It doesn't make sense to even say something like that.
And yet this postulate is prominent on various lists of postulates for quantum mechanics. I will have to do some further research to find out who is responsible for this silly idea.
This week's Dr. Bee video is on Einstein's spooky action at a distance. She says that the spookiness is the measurement update (ie, collapse of the wavefunction), not entanglement.
Believing that the wave function is a complete description necessarily causes these spooky concerns. Any observation affect distant parts of the wavefunction. If the wavefunction is a complete physical thing, then it is spooky.