That specific aspect(a persistent service worker) of fastcgi works well. but I have yet to find a compelling argument for fastcgi the protocol. let me explain.
cgi as a protocol, really a calling convention for launching processes, make sense, it fits a specific niche in the ecosystem. fastcgi does not, fastcgi is a different incompatible http, that is, fastcgi does nothing that http does better. Did we all just collectively loose our ability to think critically, locked on to the fact that the common usage was that a http server launches a cgi process and when the time came to make that process it's own service, said we need cgi for services, creating fastcgi, forgetting that http already works just fine as a service?
I am not really a back-end programmer, I am a sys-admin who sometimes makes web-based tooling. it is very possible there is a subtlety to this I missed. But I was a lot happier when I gave up on fastcgi and just made each service a http server with a reverse proxy in front to dispatch the requests.