Looking at their little toy simulation, one thing jumps out at me. Is there any particular reason that we should expect the labyrinth to not be pathological in its shape? Does the universe somehow owe it to us for it to be traversable?

One could, for instance, design the shape of the labyrinth such that most of the little jiggling dots not only can't make their way out, but also get trapped in a direction very far from the actual truth.

I hope that the random nature of the universe takes it a little easier on us than that.