Looking at what web browsers are both capable of and expected to do today I think what we really want is an "internet terminal" which would be able to contact resources over the internet, negotiate both local and remote resources for an intended purpose, and then share state bi-directionally (stateless is just zero state).
To just conjure a couple of quick examples you can imagine the differences required in providing a service that produces a simple JSON feed versus a full interactive experience that mutates a shared database. The JSON feed wouldn't require a display and could easily be consumed by autonomous agents while the other might require a minimum display size and want to use a widget set to produce controls and toolbars, etc. If my client agent is allowed access to my video display, mouse, and keyboard it could offer these to either service and allow it to respond in whatever way it feels appropriate. The JSON feed could provide a simple UI for viewing recent events, for example.
Now we do all of this today with HTML, CSS, JavaScript, etc. but none of it feels organized and all you see is re-invention after re-invention of essentially these same concepts. The fact that we even call them "applications" when they are "documents" is really what seals it to me. I personally would like to see something that is more true to the reality of computing and internet connectivity today and looks at it from a device-to-service POV. Locally I might have a graphical display, audio, and inputs but I might also have access to an SQL database or some other network-attached service. Assuming some level of trust and if negotiated properly there's no reason a remote application couldn't make use of these local resources using credentials and security profiles under my control. The can of worms here is that this is basically RPC which is the other never-ending disaster...
Internet is hard. Let's go shopping.