For starters, there are a whole load of conditions that are no less secure than a standard http connection, such as self-signed certificates. But in those cases, the browser throws up a huge and misleading warning about it being insecure. Insecure is the default on the web: we should focus on positive signs that a site is secure.
Secondly, the system should make it harder for the administrator to make mistakes. For instance, the web server could refuse to serve https on a domain that it didn't have a certificate for. Or when a certificate nears its expiry date, the administrator should be getting plenty of reminders about it.
Thinking bigger, what if we tied it closer to the sensitive UI? What if only pages loaded securely could show a password field? What if rather than typing credit card numbers into boxes on a webpage, we were used to using a special browser interface that would only light up on secure pages?