I've considered many implementations, with different types of connection methods, and this is how I view the choice.
From a developer perspective FastCGI IS out of style, in the same way they would consider C. from a developer perspective accomplishing the task can be done through simpler ways.
From an implementation perspective, HTTP isn't a perfect replacement, however their is enough overlap so they could be used to solve the same goals. BUT really this question is about implementation and architecture, and not a developer focused question, so I'll answer it from systems engineering side.
Despite what I've unfortunately read in developer blogs, FastCGI CAN be a better choice when utilized in the proper circumstances. It separates a large complicated concern, that otherwise must be implemented higher up the stack.
For example, It allows you to avoid creating a robust web server inside your framework/language. A huge task if you actually care about quality, but very doable if you slap it together like most. So it's ironically easier to roll it all up in a spaghetti ball, then cleanly separate that part. This is why so many avoid FastCGI, because they could only implement it by almost wrapping HTTP anyway, due to their bad architectural choices.
Since you didn’t get more detailed about how ambitious your plan, I can't really give you great recommendations. Let me suggest a few things to investigate, that are not the common slap together python node style.
Read about the implementation details of ,
If you want to do a more appserver model, do it right, read about