Your browser supports those things because it implements protocols, like HTTP, TLS, and others. Your browser, or other tools, could support SSH, which I think is the point of the article.
This means the author doesn't know what they're talking about, and is asking a dumb question.
The article's title is "Why aren't we using SSH for everything?", not "Why don't browsers support SSH?". Both make no sense. It's like asking why FTP clients don't support Voice-over-IP.
The article's title is "Why aren't we using SSH for everything?", not "Why don't browsers support SSH?". Both make no sense. It's like asking why FTP clients don't support Voice-over-IP.