Hello @Nibbler , thank you for reaching out.
I might have not understood the question correctly but based on the Private link documentation for Azure Front Door. The request flow is as shown below.
The incoming requests above are from public internet and Azure Front Door endpoint is accessible from internet. With Private endpoint integration Azure Front Door accesses the origin over Microsoft backbone network via private endpoint and this origin is not accessible from the internet.
Currently origin support for direct private end point connectivity is limited to Storage (Azure Blobs), App Services and internal load balancers.
Hope this answers your question! Please let me know if you have any additional questions here, I will be glad to continue with our discussion. Thank you!