A new rendering engine is indeed one of the areas of the research at tauri. For now (and until 1.0 at least) we are sticking with the webview, because we want to have an alternative to electron that is safer and is well-known enough to be stable across platforms for the foreseeable future.
Regarding what an a new engine would have to provide, as a matter of fact, Tauri does offer cross-platform APIs for the filesystem, notifications, CLI, etc. These are all rust based, and available from JS.
I do have to disagree though, in one point, and that is that your single threading comment is only true in the webview. Technically, you have the entire strength of the underlying OS available to you from rust, and that is indeed where I recommend devs do all their heavy lifting. This is one of the benefits of using a polyglot system and an inherent security benefit.