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.Tony Valenti commented
The static website hosting option is a great start but the case sensitivity is killing me:
index.html and Index.Html should both work!
Would you please provide some type of case-sensitivity options? Maybe "Convert all filenames to lowercase" or such?