Stopping DB accesses is a great way to mess up a lot of stuff. Even just stopping connections to the live website would be full of potential issues. Should it stop all access or still allow access to the administrative interface? What is the root cause of the billing overage is a report by finance or someone running a large job on EMR, should that pull the plug on the website?
What if the new services that are being suspended are writes to queuing systems that are used for order fulfillment or other business processes, should we drop these orders on the floor?
It's much easier to handle it post facto, and write off the expense on the cloud provider side, which doesn't cost them that much anyway. There are some guard rails that prevent people from doing catastrophic things that they can't write off (eg. taking all of the compute capacity of a region for hours on end, preventing other customers from actually using it) using limits that require manual intervention to be raised.