S3 -- you can't just delete customer data because they hit a billing limit
RDS -- not going to drop databases on the 27th of the month
Anything with persistent data is going to have to stay alive and accumulate costs. Admittedly these services aren't where the crazy bills come from, but it does make a simple kill switch a bit more complex.
Most service that has a limit cap will have a "grace period" of a couple of days during which the service does not work but the data is not deleted. That give your some time to get notified of the issue, and fix the problem/increase the limit.
You could factor that into the price, but then you're potentially making the price point even more unattractive to users than it already is, and users that are responsible with their budgets would be subsidizing those that aren't. Not a very workable solution.
I'd say a good solution is giving customers the option to stop accruing more storage capacity, and to have a max deadline accounted for in their budget to store data (basically each customer decides whether or not to pay for a grace period).