What the...? Does the author just not know anything about SSH, or web browsers? Why would we use SSH for everything? On top of the fact that they're entirely different protocols and tools designed for entirely different purposes, browsers already support virtually everything SSH does. File transfers, authentication, client certs, multiplexing, key pinning, etc. There is no need to use SSH, and if you did, it would be…
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.