Sorry for the lack of clarity, by "exposing the binary over the internet" I certainly wasn't implying re-implementing a HTTP server, HTTPS and certificate handling etc. You would of course have an nginx frontend that would cache the request and subtleties; the Rust FastCGI would see a well formed request, and rush to execute it just like any other dynamic language, PHP, Python.
You can of course still do stupid things inside the rust application that explode your number of concurrent requests, like waiting for slow external resources, databases etc. For a simple static formatter, it should not be the case, it would just repeatedly hit the disk cache and some minimal CPU.