>I would rather my whole system shut down and be unusable while I investigate vs. auto-scale and charge me a bill I can't cover.
Sure, but most large companies (the kind which AWS gets a lot more revenue from and cares about a lot more) want the exact opposite. Most large companies have the extra cash to spend in the case that a runwaway auto-scale was in error, but on the other hand, completely shutting down operations whenever a traffic spike happens could resort in millions of lost revenue.
>However, searching around it seems like I can only get alerts when a $$$ threshold is passed, but AWS won't take any action to stop computing or anything. Please prove me wrong.
The general advice is to use the various kinds of usage alerts (billing alerts, forecasts, etc) to trigger Lambda functions that shut down your instances as you desire. It takes a little configuration on your part, but again, AWS intentionally errs on the side of not automatically turning off your instances unless you specifically tell it to.