Remember FastCGI? (2021)

  If you find yourself with a scripted language where processing HTTP requests might be too slow or unsafe, I can still see some utility for FastCGI. For most of the rest of us, HTTP won, just write little HTTP webservers.

Without serious development effort, I would expect using an existing web server with FastCGI is faster than writing your own web server. It is also more secure as the FastCGI application can be run as a different user in a chroot, or a namespace based sandbox like a docker container.

Using HTTP does not preclude having a reverse proxy. So the only difference between FastCGI and HTTP is really what protocol your proxy and your application use, and I don't really see why FastCGI would be major win there.