One of the nice things about Rust is that it provides a lot of high-level abstraction capability in a way that doesn't impose any cost on the abstraction.
This means that, in theory, one could make a pretty good web framework in Rust that would be both quite fast and ergonomic. That said, writing those abstractions will take time, so we'll probably see lower-level HTTP libraries, followed by Express-style abstractions, followed further on by full-stack solutions like Rails.
The earlier parts of the stack are coming along quite well, so give it a few years and I think we'll have a pretty good story to tell. In the meantime, you can use Rust today very effectively as a language that you embed inside a high-level language, and I think a sizable chunk of the Rust community will use Rust for those kinds of embedding use-cases in perpetuity.
Having programmed a bit of Rust, while Rust will definitely be a very capable language for web frameworks/applications, I don't think that it'll ever be the most popular choice.
To be honest, if you think about your Rails controllers/models, 1. There isn't really all that much there(fat-models/controllers are pretty slim when you're language was built for web browsers/operating systems). 2. Think about your priorities. I can guarantee its not performance or safety. You want to build a content-rich/feature-full application. Basically, prioritize iteration speed, at all costs. No matter how good the Rust frameworks get, I don't think Rust will be the "iteration speed" language.
Meanwhile, I think, in the spirit of wycats' comment, image if ActiveRecord, Unicorn, Rack, the template renderers, etc, were all built with Rust, but still used through a Ruby interface. That would be quite the performance improvement for Rails and it would be interesting to compare its performance characteristics to a fully Rust web framework/application.
from the parent answer i would presume he thinks it's more useful as a "bottleneck fixer" in high level web frameworks. (when the bottleneck is the language of the framework).
For example, you might implement a few parts of your rails app with rust to make them faster.