Moving this work item to unplanned, as it is clear that this request is no for a global throughput limit.
We do now offer the ability to limit your maximum instances in the Premium plan, which will allow you to avoid swamping downstream resources. https://docs.microsoft.com/en-us/azure/azure-functions/functions-premium-plan#plan-and-sku-settings
We prioritized that above a max call per X limit, because our only control to limit throughput is to outright deny some number of requests above a threshold.
Keep the feedback coming!
Azure Functions Team
This feature is currently in active development. We will update this item to complete once it has shipped so those voting/commenting will be notified.
Thank you for your patience.
Thank you for the suggestion. We are working on a solution that we hope will be delivered in this calendar year.
JasonSam Bosell commented
I setup a backup and it worked one day and said "Partially Backedup" and never ran again. If the backups are not reliable, alerts really need to be added.