Storage billing is partly time-based.

EBS is billed by the second (with a one minute minimum, I think).

Once a customer hits their billing cap, either AWS has to give away that storage, have the bill continue to increase, or destroy user data.

I think most of the "horror stories" aren't related to cases like this. So we can at least agree most such stories could be easily avoided, before we looked at solutions to these more nuanced problems (one of which would be clearly communicating the mechanism of a limit and what would be the daily cost of maintaining the maxed storage - and for a free account the settings could be adjusted for these "costs" to be within free quota)