Not disagreeing entirely, but don't forget that you used to be able to type ftp://example.com and gopher://example.com into the url to access sites. I think there were others as well. Most browsers have removed those protocols.
As you point out, ftp and gopher were, at one point in time, also used to transfer websites, so the inclusion was supportive of the web directive.
But have browsers ever widely attempted to be anything other than web browsers? A couple of vendors tried including RSS support at one point, but I don't recall it catching on across the industry.
Media (images, audio, video) browsers, maybe. Technically that is not HTML, but still rendered by most browsers. However, as that content can also be embedded in HTML, requiring browser support to be present anyway, it is a bit grey area.
Late versions of Netscape and early versions of Mozilla included email clients. Mozilla later split the email client and web browser into two separate programs, Thunderbird and Firebird. Firebird became Firefox.
Last time I looked at RSS the transfer was bound to happen over HTTP. RSS is more like a web alternative. You can link from RSS to web pages, sure, but you can also link to web pages from Word documents. Perhaps browsers should all natively support .docx too?
Although you ultimately raise a good point. Most browsers do support PDF. That's the wide attempt to be something other than a web browser that I was forgetting about earlier. So, there you go, there is precedence.
Although there is still that pesky problem of most people not wanting to use RSS. Apple had good in-browser support for RSS there for a while but they found nobody used it. If Apple can't convince Average Joe to use something, it isn't likely anyone can. RSS has remained relevant for podcasts only because it has found a place in server-to-server syndication. Average Joe isn't visiting Harmony Harold's personal website to subscribe to his podcast either.
