Let me try to address your question by framing the situation. Of course this is all pure speculation, so take it for what it’s worth.
Delivering binary directly to the browser allows new e-commerce solutions (browser-based Steam, anyone?), that simply don’t exist today. I can think of several compelling ‘killer applications’ for WebAssembly, once it is sufficiently mature.
What makes WA really interesting is that it is designed to be the target of other languages. So that means you’ll be able to develop in WA from “your favorite language”. I think a mature Rust language figures prominently in that future with so many front-end developers embracing (or being forced to embrace) compiled languages for the first time. Safer code, fewer run-time bugs, better scalability AND better perf? I don’t even care what the language is called–I believe the right answer to that offering is “shut up and take my money!”
So, like others here have said, I think Rust is much more than “merely” a systems language. At this point any investment in Rust as a front-end language would be pure speculation (and a bit of a maschocistic exercise, since both Rust, WA and, presumably their debugging tools are all so young), but not a bad investment in your skillset. You’d be learning modern paradigms which would only help you if you went to Swift, Scala or even modern C++. Of course, a similar case can be made going the other way, coming to Rust.
So if you’re interested in learning new stuff, then by all means, pick an intriguing language, jump in, and don’t worry too much at this point about the “practical uses”. Pretty much regardless of what you choose, you’ll have a head start if/when WebAssembly takes off, almost no matter what language you end up developing for it in.
Personally, my bet is on Rust enjoying a material competitive advantage, but like I’ve mentioned, picking something you find interesting is more important than picking Rust, per se.