Using Japan's immediate post-war black market as an example, they exist and "function" out of necessity. Black markets form wherever the official markets cannot meet a demand. To nobody's surprise, the lack of regulation leads to abuse and scamming, but people are forced into using it because traditional forms of commerce (legal ones) are not viable. In post-war Japan, for instance, access to basic necessities like food was next to impossible through legal means, so people, even state officials, had to resort to using the black market.

I'm not an economic historian, but black markets function largely the same as regular markets, with supply, demand, competition, and monopolies. "pure trust and honor" might exist, but that's not the driving force for why black markets exist. Just as how in a regular economy a company that doesn't have a monopoly on supply risks losing out to competitors if it engages in questionable business practices, the same logic can apply to black markets, albeit with no government intervention or regulation.

Source: John Dower's Embracing Defeat.