Second chances don't exactly have a cash value; the only way to directly convert them to goods or cash is indeed The End of Battles in the Nadir.
However, that doesn't mean they're useless. There are a number of high-level challenges that are impossible to guarantee success on, even at the level cap. These are listed on the Fallen London Wiki, but a few examples include manufacturing Searing Enigmas and Impossible Theorems at the University (Watchful), "What new madness is this?" on the Listing Tower opportunity card (Dangerous), or the semi-infamous "Where did the Rosers go?" on An Unlikely Garden in the Nadir, which requires 1000(!) Persuasive for a 60% chance of success. The University business, in particular, is extremely punishing -- failing the Impossible Theorem Watchful check will kill you outright, as well as cost you a hefty chunk of change and some Sudden Insights (even if you don't use any).
Second chances were also reworked in late 2015, such that repeatedly failing the same storylet while using Second Chances will very rapidly deplete them (1, then 2, then 4, then 8, and so on) until you either succeed or give up on using Second Chances and fail. As a result, attempting to use Chances in this manner to guarantee success on the high-level challenges will very rapidly deplete your stores.