WebAssembly is open and it's intended to be a general purpose compilation target, the technologies you listed are proprietary or only intended for a single language. Also, WebAssembly's own docs state non-web embeddings as an explicit design goal[0].
As there is no commercial need for a particular corporation to prevent it, and there is no design limitation preventing it, there's no reason to assume some sort of native WASM runtime won't be available in the future. That would make it no different than Python or Ruby or any of the multitude of C++ runtimes I have to download with games on Steam.
My point being that there's no reason to assume WASM has to run as remote code connected to a server over which the user has no control or meaningful access, as opposed to a binary you can run on your desktop. There's nothing in the WASM spec that forces such a distinction to exist, that's an architectural decision made at the application level, and one that could be made in any language.
But i am not talking about such a use, i am talking about using WASM to create applications that are designed to be part of a web site and meant to be accessible only online - pretty much what the majority of Flash games did previously. The original message i replied to was about web-based applications that are meant to be delivered online so my messages were with the assumption that we are talking about web-based applications pretty much in the same vein as Google Docs or games like the thousands of Flash games you'd see out there some years ago. You wrote "That assumes it would be impossible to download a WASM blob and run it natively" - the possibility to do that would be exactly the same as downloading a JS file and run it natively (in this case i take "natively" to mean running an offline local copy in a browser without any sort of external requirement, like downloading files off the web). I do not see a reason for expecting WASM to be used in any different way.
Besides the experience the original GP post was talking about and the message i replied to didn't really leave any room for not making such an assumption since they were all about comparing web apps to native apps: " I have been thinking about why we have ended up here, and why not just native apps."
And finally, i do not see WASM being of giving any more control to the user than existing web tech - after all it relies on the rest of the webpage to work, much like JavaScript (actually, it does require JavaScript to act as a mediator - at least for the time being) and considering how you cannot download Google Docs as a native offline application to use on your desktop, despite being able to save locally the JavaScript it downloads on your browser, i fully expect to be the same situation with WASM too.