Yes, that's because time isn't actually a physical phenomenon. It's a kind of illusion, an approximation to the truth, in the same way that Newtonian mechanics is an approximation of GR in the weak-field limit. The wave function is a static, four-dimensional "thing" (it's not actually a thing, but I don't know of a more general noun). Our perception of a classical universe that evolves in "time" is not a reflection of a real underlying physical process, it's an emergent property of a sequence of subsets of the wave function in which entanglements have accumulated. Quantum information theory predicts the emergence of subsystems that are all in classical correlation with each other, i.e. a "classical universe". But none of this is actually real in a metaphysical sense.
> Time isn’t an operator
2) QM without statistical mechanics/thermo seems an odd basis to make prognostications about time or reversibility. Time isn’t an operator (see the classic Mandelstam-Tamm paper)