>> URLs are the building blocks of the web.
The web has lots of building blocks (hyperlinks, requests, the underlying protocols, HTML, and on the modern web: Javascript and XmlHttpRequest). We hide most of that implementation detail from the user because it's non-essential to the task at hand.
How essential to the task at hand is the URL for most users? I may need a building's address to find it; once I walk into the building, do I need to continuously see that address?
>> Every page has a unique URL so that you can identify it and share it with other people.
That's a significant mis-statement of what a URL is. URLs have never been unique (witness www.foo.com vs foo.com), don't necessarily identify the page (witness dynamically-generated pages that are built with information from the client's cookies or state on the server), and their utility as a sharing tool is limited to what the server allows (witness access control). They're uniform resource locators... Nothing more, nothing less.
A URL is a tool. A useful tool, certainly. But I don't keep all my useful tools constantly on display on my desk; I keep them in toolboxes until I need them. So I'd say "See how this experiment pans out."