Although I don't know how Google Chrome would use, as opposed to display, a website that started "https://www." there are sites that are not available if you do not use that prefix. Specifically, I was working at a location doing deployments where the site id for RSA tokens was https://www.<token location>.<company name>.com. Their DNS would not recognize the request if you did not include the "https://www.". I am sure that that company will truly appreciate it when Google Chrome dumps the prefix for them.