I would not pick Rust over C#/Go/Python for web development.
enum Value { Null, Bool(bool), Number(Number), String(String), Array(Vec<Value>), Object(Map<String, Value>), }
How would this look in Go?
I would say your representation is favorable when someone wants to work with arbitrary JSON in a flexible fashion. However if schemas and code generators are available, I would prefer to use those.
I'd consider a small data processing service, maybe a service invoked from the web server you're already using in Ruby or whatever, is a perfectly pleasant place to use Rust, and often likely to be 1:1 identical to those other languages.