Thank you for your feedback. We are currently in public preview of static website hosting for Azure Storage to enable this scenario. Check out the blog post here for more details: https://azure.microsoft.com/en-us/blog/azure-storage-static-web-hosting-public-preview. The feature set includes support for default documents and custom error documents for HTTP status code 404.
For any further questions, or to discuss your specific scenario, send us an email at firstname.lastname@example.org.Jack Guy commented
C'mon Microsoft. I'm going to have to move to S3 and I really don't want to...