That's not true. It's a "single page app" with built in support for both pushState and hash-based URLs, so there's no reason anything needs to reinitialize just to update the URL.

I have written an Ember app that maintains a persistent websocket connection as it transitions around through many URLs.

No, you're doing it wrong. Apart from your controllers being long-lived and persist between routes, you're usually interacting with the data store, which caches and keeps references to records. Just make sure you're pushing data into the store instead of making requests or whatever. Also, remember the Run Loop.