Time reversibility exists in quantum mechanics because observables are self adjoint operators. Closed systems evolve unitarily. In simpler terms, you can think of it as the requirement that maps preserve distances and are easily invertible. We need this so that the information describing a system (which we can still talk about in terms of traces), remains invariant with time. In the classical sense, the corresponding violation leads to probabilities not summing to 1! We clearly can't have information shrink and for pure systems, dropping distance preserving maps leads to a really awesome universe (I believe this also ends up highly recommending L2). We literally go from a universe that is almost certainly near the bottom end of the Slow Zone of Thought to the Upper Beyond (https://en.wikipedia.org/wiki/A_Fire_Upon_the_Deep#Setting). We gain non-locality, causality violations and powerful computational ability.
In practice, our confusion about a system does increase with time as classical systems become ever more correlated, losing distinguishability, aka decoherence.
In practice, our confusion about a system does increase with time as classical systems become ever more correlated, losing distinguishability, aka decoherence.