I have an application whose primary function works in real time, through websockets or long polling.
However, most of the site is written in a RESTful fashion, which
WebSockets (or long polling) based transports mostly serve for (near) real-time communication between the server and client. Although there are numerous scenarios where these kinds of transports are required, such as chat or some kind of real-time feeds or other stuff, not all parts of some web application need to be necessarily connected bidirectionally with the server.
REST is resource based architecture which is well understood and offers it's own benefits over other architectures. WebSockets incline more to streams/feeds of data in real-time which would require you to create some kind of server based logic in order to prioritize or differentiate between resources and feeds (in case you don't want to use REST).
I assume that eventually there would be more WebSockets centric frameworks like socketstream in the future when this transport would be more widespread and better understood/documented in the form of data type/form agnostic delivery. However, I think, this doesn't mean that it would/should replace the REST just because it offers functionality which isn't necessarily required in numerous use cases and scenarios.