[downplay]

They have application in URIs. And there is a matter of building trust relationships through them. The domain alone isn't enough to do that. I tend to lean on search engines to affirm the genuineness of a domain.

Domain names provide an abstraction in that you can hide web services behind them with routing, ports and protocols.

Personally I'd rather something like the Star Trek computer interface and not care about domain names and urls.

Me: Computer, surmise the article by Foo Bar about Such and Such please.

If ambiguities were presented the computer would interrogate me to help filter them. The computer being the interface abstracting away how and where the info came from. Unless I asked of course! This isn't a million miles away from a modern search engine, it's just I have to do further filtering/querying.