I thought it suffered from darkness-induced audience apathy to such an extent that it was ludicrous
Note that episode came from Sandman #6, which was published in 1989. So, with that in mind I don't feel that "audience apathy" was at play.
Back in the late 80s, Gaiman, Moorcock, and Moore were the tip of the spear in terms of writing hard-hitting content that challenged readers. I also think that Sandman #6 "24 hours" was definitely an idea that later lead to American God's.
The point behind episode 5 (and the 24 hours story) was to display just how much chaos a godlike power could unleash on a small scale. The terror of it doesn't need to be unveiled on some global, cataclysmic scale. Simply opening up people to let go of their inhibitions and no longer ignore the little impulses led to unfettered truth.
Example. It wasn't that those characters were so dishonest with themselves that by simply being honest all this edgy stuff happened. There are reasons why people don't answer their every urge, or tell a white lie, or choose against their desires. That one character ended up fucking another and then violence happens wasn't the point. The POINT was that giving into your impulses 100% means you fuck the cook, and then when you get angry you react to that, and then you react to every impulses, be it dread, relief, and it ends up becoming an inescapable quicksand. Such chaos can start out to create something beautiful and then unravel out of control, and thus the whims of a shortsighted man with godlike power spells doom for everyone he comes into contact with.
The concept of 24 hours was written at a time where Alan Moore was challenging the concept of civil rights in V for Vendetta and the deep questions of the Watchmen. Gaiman is a different breed of writer and at the time 24 hours was published it was shockingly unapologetic and unafraid to touch these themes.