Tl;dr: URLs are necessary, but we could do better in hiding implementation details (protocols, certificates..) to the average users
The way I see it, urls are nothing more than identifiers. They are unique, meaningful names, which leak implementation details (protocol used, query parameters, ecc) to the final users who, at least here in Italy, couldn’t know less about HTTPS, certificates, GET query parameters or that cool stuff we all like to think about.
To the average user, “facebook.com/user/12345&today=true” means “Facebook"
So I’m totally with you when you say that URLs might not be the best UI for the average user! To me the browser’s search bar and your bookmarks are nothing more than an app store and an app drawer in a mobile OS! You search for things, then you decide to “keep” some of those. It’s the os’s job then giving you the info on where you are, security alerts, and so on.
There’s one really important thing we’d lose by giving up on URLs, and that would be freedom. URLs give people control, they can use a different bookmarking mechanism if they so choose, for instance. In the mobile example I made, users can only do what the OS allows them to do.
Take a podcasting app, it needs the feed’s url in order to add your podcast to its list, and that’s easily done when you can simply copy and paste the address. How can an android app query another app’s specific page content? It’s an hard problem, only partially solved by intents.
Anyway, I think we all agree that removing URLs from the equation would be crazy and unacceptable after all these years people (and software!) got used to rely so heavily on those. However, I believe we can (and should?) do a better job hiding those ugly identifiers from the average user’s journey; I am sure that HTML semantics, meta tags and so on can give the browser enough hints to be able to at least show a different breadcrumb: Facebook > Profile page > Alessandro Menduni, or Amazon > Checkout > Shipping info
Edit: re-reading my answer, I think it came out a little bit strong or pretentious. I apologize for that, English is not my first language and I realize I wasn’t able to set the tone I wanted to set!
I simply wanted to add my voice to the conversation and, if you can, please spend some time telling me why you disagree with my vision ☺