Rest is a structured description of how html/http/web work sorta. An example of a non rest aspect of how a webpage works is how the favicon is by default fetched by a well known url, or how cookies use a magic list of domains to decide if two origins are similar enough or not.

Other than things like this the browser makes very little assumptions about how a website works, it just loads what the html tells it to load and shows the content to the user. Imagine the alternative where browser by default assumed that special pages example.com/login and example.com/logout existed and would sometimes navigate you there by themselves (like with a prompt "do you want to login?")

If you wanted to design a new improved html alternative from scratch you likely would want the same properties.

The issue with Rest API is that most of what we call API are not websites and most of their clients are not browser but servers or the JavaScript in the browser where IDs are generally more useful than links.

REST is incredibly successful, html is rest, CSS is rest, even JavaScript itself is rest, but we do not call APIs that return html/CSS/js/media APIs we call them websites