Part of Jack's allure as a character is his moral ambiguity. I think if they had explored this plot thread it would have shifted him from "might get around to doing the right thing…if he feels like it" to "officially a good guy." Just my hypothesis, anyways.

Or at the end when he’s about to be hung, and the guy has a literal laundry list of his offences.
"The crimes for which you are to be hanged include: three cotton shirts, two pairs of ugly striped shots, a full set of king-size bedsheets, half a dozen pairs of underwear…"