A somewhat related naive question: is anyone using FastCGI (or just CGI) to interface directly with a web server like Apache, NGINX, or Caddy for their web apps? What reasons would you choose to not interface with use these web servers directly?

These web servers are battle-tested and feature-rich. If you add another layer like an application server (Puma, Gunicorn etc) that sits between the server and your programming language does the application server end up duplicating some (most?) of the functionality of the web server?