"You accrue interest on paper, but the bank never has enough capital to cover that paper."

That is true, but aren't a lot of things setup that way? Technically they have no means to fully comply with their obligations at any given time. And that reminds me of fitness clubs. Take your local fitness club for example, that can perhaps facilitate 100 or so members at any given time, yet those clubs will often sell 1000s of memberships. Imagine if all those members showed up at one time!!! :)