So you hit your limit. Is all your storage deleted? You can't receive an alert because that costs something (even if it's a fraction of a cent) to send. Are your domains forfeit? Audit logs destroyed? There's no reasonable way to implement this. Billing alerts are the best you can do on this problem and I think it would be a good faith move for AWS to enable some by default but a limit just doesn't make sense on any level.
EDIT: Lots of people proposing solutions that work for them. AWS has to think of everyone. And they did. That's why budget alerts exist and you can respond in the way you choose. Everyone's conflicting ideas for how to solve this can be implemented today on top of billing alerts/actions[1]. Case closed.
[1] https://aws.amazon.com/blogs/aws-cost-management/get-started...