Ideally, the web would be an ecosystem built on standards, allowing anyone to build their own browser and read content on the web. In practice, the task of building (and maintaining!) a web browser is so difficult that only a few organizations can manage it: Microsoft, Mozilla, and a consortium of other companies and browsers that rally around WebKit/Blink (Opera, Vivaldi, Chrome/Chromium, Safari). This means that compared with other standards (calendars, text editors, image editors, and even spreadsheets), there are relatively few choices in the market for browsers, simply due to the overwhelming cost of building and maintaining such a hugely complex piece of software.
Such a text-based browser probably won't be suitable for general web browsing, but can be very effective for large subsets of browsing activity. Reading the news, searching the web, reading reference materials, and doing research are all a good fit for text-based browsing, and text-based browsers can seamlessly integrate with existing workflows more readily than their graphical counterparts.
By lowering the barriers to entry and maintenance, targeting a subset of web standards allow more browsers be created that flesh out the browser ecosystem, which in turn embeds the web as a first-class citizen in our computing environment, rather than relegating it to the Chrome/Firefox/Safari sandbox.
Use cases vary, naturally. I've found that eww is very effective for searching the web, reading Ruby, Python, and Postgres documentation, as well as Wikipedia, Hacker News and most news sites (especially with
eww-readable, which was added in Emacs 25). Blogging with it is particularly effective because of the fast context switching, unified killring and rapid search through web pages via
Most sites don't design with text interfaces in mind, but they should. Hacker News is a fantastic example of how sites should look in text browsers.