I think if Chrome changes to the omnibox really click. The need for SPA in general will dwindle. You cannot see the URL so if it is ugly who cares. And if the page refreshes fast enough most end users will not be able to tell you are on a SPA or not.
SPA has nothing to do with URL. If your SPA uses a routing/history solution so deeplinks and history and the back button work properly (and it should), it's exactly, in terms of URLs, like what you'd naively expect from a non-SPA app.
What is displayed in the URL has nothing to do with SPAs. Go to Twitter. It is an SPA. The URL changes on every click, just like basically all modern SPAs.