I suspect that the reason it doesn't work is that the theory is off. Lack of the initial capital (to bootstrap the virtuous cycle) is not the real bottleneck; it's the ability to commit to a plan where there is a big long-term benefit. Such a charity would run into the same problems as for-profit lenders and CCs -- not enough people paying back the money.
On the other hand, the $200-300 being charged might represent a risk level of the whole class of rentals being made... it's hard to know without on the ground information.
Of course, using Amazon requires Internet access, which can also be a problem.
One thing I both do understand and lament is how the more impoverished communities are culturally tuned to turn on each other than work together. If your household is too poor to afford a lot of the things that are taken for granted - a working kitchen, for example - having four neighbors work together to have one working kitchen they could all share and set up time slots to use would go a long way to getting out of poverty.
But you really just cannot rely on other people in those situations. Its a prisoners dilemma where the prison is poverty. It takes one person taking advantage of cooperation to ruin it.
There's also the fact that if you can't afford to bulk buy a few extra rolls of TP, you sure as hell can't afford a quarter of a kitchen.
People seem to forget when they talk of the poor: "If only they invested in X, Y, or Z". The whole point of someone struggling financially is that they CANNOT invest, because they have zero, and often negative "extra" money. "Paycheck to paycheck" is not a euphemism, it's a literal situation. Even one missed hour of pay is devastating to these people.
Poor people who have close enough personal relationships to justify trust share resources all the time (source: spent several years in my late childhood in a family on welfare in public housing.)
Now, lots of poor people don't have close relationships with people with resources to share, and arms-length contracts with resort to the courts for enforcement don't work for them when personal trust isn't enough, because they can't afford the cost and delays of enforcement.
Again, it's expensive to be poor.
I'm guessing that at the prices the parent listed, the person isn't buying a $70k luxury car for $1000+ a month, but has bad credit and can't put any money down on the car so they're going to radically overspend. I'm really hoping that it's a late model Honda or Toyota that will go 300,000 miles and not something that was salvaged.
My mom pays 200-300 a WEEK for her car. Many people on here would say that's a terrible idea and she should just buy a cheaper used car for 1000-2000 dollars, but they don't realize she needed the car NOW or she'd lose her job and she doesn't have that cash laying around. No one would give her a normal loan and none of us could afford to help her at the time. It really seems the only people in the world willing to help her are the people that need 200-300 a week to sell her a car. And that's just the car. Housing, food, clothes, and nearly everything else can be explained with the same rationale.
Your line here is key: "Too often, we assume that poor people make poor choices, without considering that they might actually be making the best of the shitty slate of options available to them."