I dunno, your logic is sound for people who are not in desperate straits, but people make significantly altered (but still rational) risk assessments under duress. If such people are able to get short term funding at any cost, even if they know they can’t repay it, then the personal risk of the consequences of that decision could well rank far lower than the consequences of the alternative, which is for example that your kids starve. That has nothing to do with literacy or saving people from themselves and more to do with access to emergency funding and information.

Even if we accept that payday lending has a place, I think most payday lenders benefit from this equation and certainly contribute to the poverty trap: even if most of the debtors end up getting (likely minimum wage) jobs, they now have the added burden of repaying the onerous rates that they agreed to while under extreme duress. And that duress is the thing that seems to be missing in your calculus.

The problem with payday loans is not the theoretical application of debt theory but the rational risk taking of people with no other (perceived) options: under almost all circumstances, it is better to be starving next week than it is to be starving today.