Besides, Azure proves that it's clearly possible. Azure have a cap. MSDN gives you free Azure credits. When you open an account via MSDN you still have to put in payment details, but you have the option to enable a hard cap that prevents you spending past your free credits. So Azure have clearly got a solution for stopping all the services when the credit limit is reached.
All of what you describe as problems are just decisions to be made. S3 data..? Delete it. Make it read only. Pretend to delete it, but make recovery possible for x days. Doesn't really matter, just pick one when you build it, and document what it does. People who want a cap are going to more concerned with the overspend than any data or service integrity. They could stick up a disclaimer... "If you enable this cap you data may be destroyed or corrupted if your spending reaches the cap". There are solutions to the implementation problem.
Besides, they probably already have all this code in place. If your payment methods gets declined I'm prepared to bet Amazon don't just let all your services continue running indefinitely because shutting them down automatically is too hard of a problem for them to solve. So any cap could be implemented by just triggering the payment declined function.
