How is that your conclusion? If you set up proper monitoring, you'll be notified and able to turn things off by the time you've been cost $10. I would hardly call that catastrophic...
If I missed the notification that an infinite loop was costing 13 cents a minute by the end of the day I am out almost 190$. I know the rational that Amazon has is that you would want to scale your service if you were adding hundreds of people in a single day but thats a lot less likely than an error in my code flushing a relatively considerable amount of money down the toilet. If that was not a risk though I would be using Lambda, it otherwise seems like my best option. Backend is not my forte though so if the point seems crazy I'm willing to consider any advice.
AWS will send billing alert notifications via SNS. Theoretically, you could write a script to listen to the alert queue and shut down processing if you breach a pre-defined threshold.
Of course, you then need to make sure your billing script successfully terminates any processes that are costing money.
I'd love to see AWS implement hard cost limits for services like this. e.g. specify you want to spend a maximum of $10/day, and once you reach that limit your service is temporarily suspended.