Rust is a wonderful system programming language. However, it has its shortcomings, especially when it comes to string manipulation and handling of different or unknown data types. JavaScript and PHP are awesome languages when it comes to those.
The next problem with Rust is that you will have to develop your own non-blocking threading model. That alone is a very big task, which Node.JS solves formidably. Node.JS can easily hold connections to millions of clients while being very responsive!
In Addition, most crates are still in very early development. They are not ready for production, yet. If you don't plan on inventing the wheel all over in a lot of places, don't use Rust.
Last but not least, Rust "IDEs" (tbh, there are none and the plugins are lacking) are missing a lot of features which might be important for developers who want to be productive, namely auto-complete, docs preview and debugging capabilities. I don't think you can be as productive as with other languages just yet.
So, while the above points sound mostly negative, I encourage you to write a Rust application, if you use it as a number cruncher in you web application, but write the I/O part with something else.