As long as there has been Javascript there has been a dream that you could write your front end and back end in the same language. This is realized in the form of node.js (run Javascript on the back end) as well as numerous solutions such as GWT (compile Java to Javascript), Silverlight (write C# for the front end), etc.
None of these systems have really gone mainstream though.
Rust isn't great for everything. The macro system is very limited compared to Lisp, don't expect to make great DSLs while staying in the language. You'll notice a lot of Rust game projects still feel compelled to embed a separate scripting language.
None of these systems have really gone mainstream though.