Is this universally true – i.e. baked in to the wasm spec – or is it just true in a browser environment? Consider things like NW.js[1] or Electron[2] – might we see cross platform apps being developed where all or parts of it are written in <insert language here> and compiled to wasm, then packaged up with a runtime and delivered as a "native" application for desktop, mobile, or whatever?
No, the wasm spec doesnt mention web standards at all. It can be implemented without a JavaScript VM nearby, and at the moment isn't even capable of interacting with the DOM/JavaScript APIs directly when it is run in web browsers.
I probably should have specified but I was referring to GUI applications specifically. For things without a GUI, or that require deeper system integration than you get with these runtimes you're absolutely right – there's little point. But for a very large class of GUI applications it makes a lot of sense, working with technologies that not only have stood the test of time and are good enough for plenty of use cases, but also mean you can with very little effort package your application for multiple operating systems. Some of these applications will need stronger performance than can be provided by the JS engine, so hence the question re: wasm.
[1]: https://nwjs.io
[2]: https://electron.atom.io