Nae trivial parts
A site's domain is under control of the administrator. It is the administrator who decides what is and what is not trivial.
If an administrator decides that the www in http://www.example.com is superflous then they will serve the site on http://example.com (yes, this admin has also decided against compulsory TLS use).
The browser's job is to show where the user is at, not trying to pull an "I know better" in the name of God knows what.