The problem is that you're thinking of extensions as files, which most users don't understand. They want an extension; they don't care how it's delivered and they have no idea what an auto-update source is.
I have a button on my website that says "Install extension." I don't tell them it's a link to a .CRX file; that's an implementation detail. If you asked any of my users whether they had downloaded a file (let alone what its extension is), most couldn't tell you. Similarly, the Chrome Web Store has buttons that say "Add to Chrome," not "Download Trusted .CRX File."
I have a button on my website that says "Install extension." I don't tell them it's a link to a .CRX file; that's an implementation detail. If you asked any of my users whether they had downloaded a file (let alone what its extension is), most couldn't tell you. Similarly, the Chrome Web Store has buttons that say "Add to Chrome," not "Download Trusted .CRX File."