I'm not sure it is a "quaint" idea that URLs convey or contain information. Sure, you've got bad sites that tell you nothing (/file.cgi?id=1234¶m=abcd) and you've got very popular sites with URLS that are just as bad (Amazon), but you've also got a vast number of sites with human readable URLs, programming platforms/frameworks that encourage and facilitate human readable URLs, and big/popular sites who have recently moved or are currently moving in the direction of replacing their bad URLs with meaningful ones.
It also used to be the case that human-readable URLs had an impact on how search engines ranked your site... I'm not sure if that's true anymore. Especially since that's been so gamed by portal and spam sites.
Amongst professional web developers, human-readable URLs are a known best practice. However, the web moves at such high velocity that we are constantly being joined by wave after wave of new developers... and there is no certification program and no test. Anybody can be a web dev. (That's actually one of the coolest parts of the web as a platform.)
I'm particularly concerned that once URLs are no longer visible, web developers -- particularly new web developers -- will take this as an indication that URLs have no importance. This will manifest in at least two ways: more sites with non human-readable URLs and more sites with many screens/pages but only one URL.
Human-readable URLs are a very handy power-user tool because people who understand URLs can navigate directly to certain things by intelligent guessing. They are also quite handy for regular users in the context of bookmarking or link sharing in the cases where the page title has not replaced the URL as the identifier. However, I imagine that fewer and fewer people are sharing raw URLs now. I imagine that people are more often clicking a share button which means that the URL is already deemphasized, and instead a title/snippet/snapshot is being shared and used to identify the content.
URLs in general, human-readable or not, are currently still very important and essential to the web ecosystem for the above use cases of sharing and bookmarking. If a vast array of content is all accessible through a dynamic experience but all at a single URL, then that content cannot be shared or bookmarked directly. Only the entryway into the content can be shared. That starts to breakdown the very fabric of the web.
If developers stop taking URLs seriously in general, at first they will run into SEO, discoverability, share-ability, and usability problems. But, if Google and some other big players decide to provide solutions to those problems that are not URL-based, then the URL will really suffer some serious blows.
I dunno though... underneath every major OS is still a path-based navigational tree. I think we'll always invent ways to discover and navigate without having to know or see the paths, but the software developers will still be using and implementing paths underneath.
All this to say... the hiding of URLs could be a serious blow to the future of human-readable URLs. But for technical reasons, it is probably not a blow to the idea of URLs in general.
But, I do not think we should encourage the idea that the URLs-as-useful-information battle is already lost. More information is always objectively better than less information. URLs that convey information are objectively better than URLs that only identify a resource through internal unique id numbers. We would be horrified if our desktop software we use to manage our music and other media created nonsense file folders like /12345/989898/ababab/. We should be equally horrified when website URLs look like that.