Roasts, in their standard form, thrive on chaos. They give speakers the green light to share the unfiltered truth of the night’s subject — or, more often, an exaggerated interpretation — leading to story after story, joke after joke, screed after screed that crosses the boundaries of accepted social mores. But, despite certain selections for Comedy Central’s (in)famous televised events, roasts typically work best when the roastee is well-liked. After all, it’s supposed to be an honor. Sure, taking a jackass to task can be fun, but there’s added excitement to peeking behind the curtain of an everyman’s gracious public image, just as there’s an added challenge for comedians to hit a not-so-easy target.

“Yearly Departed,” Amazon Prime Video’s end-of-year comedy special that says goodbye to “the year we love to hate,” is not officially a roast. It’s a wake. Speakers Tiffany Haddish,...